Algebraic Expressions

An algebraic expression containing three terms is called a
A. monomial

B. binomial

C. trinomial

D. All of these

Number of terms in the expression 3x²y – 2y²z – z²x + 5 is
A. 2

B. 3

C. 4

D. 5

The terms of expression 4x² – 3xy are:
A. 4x² and –3xy

B. 4x² and 3xy

C. 4x² and –xy

D. x² and xy

Factors of –5x² y² z are
A. – 5 × x × y × z

B. – 5 × x²× y × z

C. – 5 × x × x × y × y × z

D. – 5 × x × y × z²

Coefficient of x in – 9xy²z is
A. 9yz

B. – 9yz

C. 9y²z

D. – 9y²z

Which of the following is a pair of like terms?
A. –7xy²z, – 7x²yz

B. – 10xyz², 3xyz²

C. 3xyz, 3x²y²z²

D. 4xyz², 4x²yz

Identify the binomial out of the following:
A. 3xy² + 5y – x²y

B. x²y – 5y – x²y

C. xy + yz + zx

D. 3xy² + 5y – xy²

The sum of x⁴ – xy + 2y² and –x4+ xy+2y² is
A. Monomial and polynomial in y

B. Binomial and Polynomial

C. Trinomial and polynomial

D. Monomial and polynomial in x

The subtraction of 5 times of y from x is
A. 5x – y

B. y – 5x

C. x – 5y

D. 5y – x

– b – 0 is equal to
A. –1 × b

B. 1 – b – 0

C. 0 – (–1) × b

D. – b – 0 – 1

The side length of the top of square table is x. The expression for perimeter is:
A. 4 + x

B. 2x

C. 4x

D. 8x

The number of scarfs of length half metre that can be made from y metres of cloth is :
A. 2y

B.

C. y + 2

D.

123x²y – 138x²y is a like term of :
A. 10xy

B. –15xy

C. –15xy²

D. 10x²y

The value of 3x² – 5x + 3 when x = 1 is
A. 1

B. 0

C. –1

D. 11

The expression for the number of diagonals that we can make from one vertex of a n sided polygon is:
A. 2n + 1

B. n – 2

C. 5n + 2

D. n – 3

The length of a side of square is given as 2x + 3. Which expression represents the perimeter of the square?
A. 2x + 16

B. 6x + 9

C. 8x + 3

D. 8x + 12

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Sum or difference of two like terms is ______ .

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In the formula, area of circle = πr², the numerical constant of the expression πr² is _____ .

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3a²b and –7ba² are _____ terms.

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–5a²b and –5b²a are ______ terms.

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In the expression 2πr, the algebraic variable is ______ .

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Number of terms in a monomial is ______.

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Like terms in the expression n(n + 1) + 6 (n – 1) are ____ and _____.

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The expression 13 + 90 is a _____ .

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The speed of car is 55 km/hrs. The distance covered in y hours is ______.

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x + y + z is an expression which is neither monomial nor ________ .

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If (x²y + y² + 3) is subtracted from (3x²y + 2y² + 5), then coefficient of y in the result is _______ .

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– a – b – c is same as – a – (________).

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The unlike terms in perimeters of following figures are ______ and _____.

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On adding a monomial ________ to – 2x + 4y² + z, the resulting expression becomes a binomial.

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3x + 23x² + 6y² + 2x + y² + ______ = 5x + 7y².

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If Rohit has 5xy toffees and Shantanu has 20yx toffees, then Shantanu has _____ . more toffees.

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x is a polynomial.

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(3a – b + 3) – (a + b) is a binomial.

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A trinomial can be a polynomial.

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A polynomial with more than two terms is a trinomial.

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Sum of x and y is x + y.

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Sum of 2 and p is 2p.

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A binomial has more than two terms.

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A trinomial has exactly three terms.

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In like terms, variables and their powers are the same.

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The expression x + y + 5x is a trinomial.

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4p is the numerical coefficient of q² in – 4pq².

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5a and 5b are unlike terms.

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Sum of x² + x and y + y² is 2x² + 2y².

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Subtracting a term from a given expression is the same as adding its additive inverse to the given expression.

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The total number of planets of Sun can be denoted by the variable n.

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In like terms, the numerical coefficients should also be the same.

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If we add a monomial and binomial, then answer can never be a monomial.

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If we subtract a monomial from a binomial, then answer is at least a binomial.

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When we subtract a monomial from a trinomial, then answer can be a polynomial.

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When we add a monomial and a trinomial, then answer can be a monomial.

Write the following statements in the form of algebraic expressions and write whether it is monomial, binomial or trinomial.

(a) x is multiplied by itself and then added to the product of x and y.

(b) Three times of p and two times of q are multiplied and then subtracted from r.

(c) Product of p, twice of q and thrice of r.

(d) Sum of the products of a and b, b and c and c and a.

(e) Perimeter of an equilateral triangle of side x.

(f) Perimeter of a rectangle with length p and breadth q.

(g) Area of a triangle with base m and height n.

(h) Area of a square with side x.

(i) Cube of s subtracted from cube of t.

(j) Quotient of x and 15 multiplied by x.

(k) The sum of square of x and cube of z.

(l) Two times q subtracted from cube of q.

Write the coefficient of x2 in the following:

(i) x² – x + 4

(ii) x³ – 2x² + 3x + 1

(iii) 1 + 2x + 3x² + 4x³

(iv) y + y²x + y³x² + y⁴x³

Find the numerical coefficient of each of the terms:

(i) x³y²z, xy²z³, –3xy²z³, 5x³y²z, –7x²y²z²

(ii) 10xyz, –7xy²z, –9xyz, 2xy²z, 2x²y²z²

Simplify the following by combining the like terms and then write whether the expression is a monomial, a binomial or a trinomial.

(a) 3x²yz² – 3xy²z + x²yz² + 7xy²z

(b) x⁴ + 3x³y+3x²y²–3x³y–3xy³+y⁴– 3x²y²

(c) p³q²r + pq²r³ + 3p²qr² – 9p²qr²

(d) 2a + 2b+2c–2a–2b–2c – 2b + 2c + 2a

(e) 50x³ – 21x + 107 + 41x³ – x + 1 – 93 + 71x–31x³

Add the following expressions:

(a) p² – 7pq – q² and – 3p² – 2pq + 7q²

(b) x³–x²y–xy² –y³ and x³ –2x²y+3xy²+4y

(c) ab + bc + ca and – bc – ca – ab

(d) p² – q + r, q² – r + p and r² – p + q

(e) x³y² + x²y³ +3y⁴ and x⁴ + 3x²y³ + 4y⁴

(f) p²qr + pq²r + pqr² and – 3pq²r –2pqr²

(g) uv – vw, vw – wu and wu – uv

(h) a² + 3ab – bc, b² + 3bc – ca and c² + 3ca – ab

(i) p⁴ + 2p² + -17p + p² and

(j) t – t² – t³ – 14; 15t³ + 13 + 9t – 8t²; 12t² – 19 – 24t and 4t – 9t² + 19t³

Subtract

(a) –7p²qr from – 3p²qr.

(b) –a² – ab from b² + ab.

(c) –4x²y – y³ from x³ + 3xy² – x²y.

(d) x⁴ + 3x³y³ + 5y⁴ from 2x⁴ – x³y³ + 7y⁴.

(e) ab – bc – ca from – ab + bc + ca.

(f) –2a² – 2b² from – a² – b² + 2ab.

(g) x³y² + 3x²y² – 7xy³ from x⁴ + y⁴ + 3x²y² – xy³.

(h) 2(ab + bc + ca) from –ab – bc – ca.

(i) 4.5x⁵ –3.4x²+5.7 from 5x⁴–3.2x²–7.3x.

(j) 11 – 15y² from y³ – 15y² – y – 11.

(a) What should be added to x³ + 3x²y + 3xy² + y³ to get x³ + y³?

(b) What should be added to 3pq + 5p²q² + p³ to get p³ + 2p²q² + 4pq?

(a) What should be subtracted from 2x³ – 3x²y + 2xy² + 3y³ to get x³ – 2x²y + 3xy² + 4y³?

(b) What should be subtracted from –7mn + 2m² + 3n² to get m² + 2mn + n²?

How much is 21a³ – 17a² less than 89a³ – 64a² + 6a + 16?

How much is y⁴ – 12y² + y + 14 greater than 17y³ + 34y² – 51y + 68?

How much does 93p² – 55p + 4 exceed 13p³ – 5p² + 17p – 90?

To what expression must 99x³ – 33x² – 13x – 41 be added to make the sum zero?

Subtract 9a² – 15a + 3 from unity.

Find the values of the following polynomials at a = – 2 and b = 3:

(a) a² + 2ab + b²

(b) a² – 2ab + b²

(c) a³ + 3a²b + 3ab² + b³

(d) a³ – 3a²b + 3ab² – b³

(e)

(f)

(g)

(h) a² + b² – ab – b² – a²

Find the values of following polynomials at m = 1, n = –1 and p = 2:

(a) m + n + p

(b) m² + n² + p²

(c) m³ + n³ + p³

(d) mn + np + pm

(e) m³ + n³ + p³ – 3mnp

(f) m²n² + n²p² + p²m²

If A = 3x² – 4x + 1, B = 5x² + 3x – 8 and C = 4x² – 7x + 3, then find:

(i) (A + B) – C

(ii) B + C – A

(iii) A + B + C

If P = –(x – 2), Q = –2(y +1) and R = –x + 2y, find a, when P + Q + R = ax.

From the sum of x² – y² – 1, y² – x² – 1 and 1 – x² – y² subtract – (1 + y²).

Subtract the sum of 12ab –10b² –18a² and 9ab + 12b² + 14a² from the sum of ab + 2b² and 3b² – a².

Each symbol given below represents an algebraic expression:

= 2x² + 3y, = 5x² + 3x, = 8y² – 3x² + 2x + 3y

The symbols are then represented in the expression:



Find the expression which is represented by the above symbols.

Observe the following nutritional chart carefully:



Write an algebraic expression for the amount of carbohydrates in ‘g’ for

(a) y units of potatoes and 2 units of rajma (b) 2x units tomatoes and y units apples.

Arjun bought a rectangular plot with length x and breadth y and then sold a triangular part of it whose base is y and height is z. Find the area of the remaining part of the plot.

Amisha has a square plot of side m and another triangular plot with base and height each equal to m. What is the total area of both plots?

A taxi service charges ₹ 8 per km and levies a fixed charge of ₹ 50. Write an algebraic expression for the above situation, if the taxi is hired for x km.

Shiv works in a mall and gets paid ₹ 50 per hour. Last week he worked for 7 hours and this week he will work for x hours. Write an algebraic expression for the money paid to him for both the weeks.

Sonu and Raj have to collect different kinds of leaves for science project. They go to a park where Sonu collects 12 leaves and Raj collects x leaves. After some time Sonu loses 3 leaves and Raj collects 2x leaves. Write an algebraic expression to find the total number of leaves collected by both of them.

A school has a rectangular play ground with length x and breadth y and a square lawn with side x as shown in the figure given below. What is the total perimeter of both of them combined together?

The rate of planting the grass is ₹ x per square metre. Find the cost of planting the grass on a triangular lawn whose base is y metres and height is z metres.

Find the perimeter of the figure given below:

In a rectangular plot, 5 square flower beds of side (x + 2) metres each have been laid (see figure given below). Find the total cost of fencing the flower beds at the cost of ₹ 50 per 100 metres:

A wire is (7x – 3) metres long. A length of (3x – 4) metres is cut for use. Now, answer the following questions:

(a) How much wire is left?

(b) If this left out wire is used for making an equilateral triangle. What is the length of each side of the triangle so formed?

Rohan's mother gave him ₹ 3xy² and his father gave him ₹ 5(xy²+2). Out of this total money he spent ₹ (10–3xy²) on his birthday party. How much money is left with him?

(i) A triangle is made up of 2 red sticks and 1 blue sticks . The length of a red stick is given by r and that of a blue stick is given by b. Using this information, write an expression for the total length of sticks in the pattern given below:



(ii) In the given figure, the length of a green side is given by g and that of the red side is given by p.



Write an expression for the following pattern. Also write an expression if 100 such shapes are joined together.

The sum of first n natural numbers is given by Find

(i) The sum of first 5 natural numbers.

(ii) The sum of first 11 natural numbers.

(iii) The sum of natural numbers from 11 to 30.

The sum of squares of first n natural numbers is given by or Find the sum of squares of the first 10 natural numbers.

The sum of the multiplication table of natural number ‘n’ is given by 55 × n. Find the sum of

(a) Table of 7

(b) Table of 10

(c) Table of 19

If = 2x + 3, x + 7 and = x – 3, then find the value of :

i.

ii.

If and = x + 6, then find the value of:

i.

ii.

Translate each of the following algebraic expressions

4b – 3

Translate each of the following algebraic expressions

8(m + 5)

Translate each of the following algebraic expressions

Translate each of the following algebraic expressions

(i) Critical Thinking Write two different algebraic expressions for the word phrase “ of the sum of x and 7.”

(ii) What’s the Error? A student wrote an algebraic expression for “5 less than a number n divided by 3” as What error did the student make?

(iii) Write About it Shashi used addition to solve a word problem about the weekly cost of commuting by toll tax for ₹ 15 each day. Ravi solved the same problem by multiplying. They both got the correct answer. How is this possible?

Challenge Write an expression for the sum of 1 and twice a number n. If you let n be any odd number, will the result always be an odd number?

Critical Thinking Will the value of 11x for x = –5 be greater than 11 or less than 11? Explain.

Match Column I with Column II in the following:

At age of 2 years, a cat or a dog is considered 24 “human” years old. Each year, after age 2 is equivalent to 4 “human” years. Fill in the expression [24 + 4(a – 2)] so that it represents the age of a cat or dog in human years. Also, you need to determine for what ‘a’ stands for. Copy the chart and use your expression to complete it.

Express the following properties with variables x, y and z.

(i) Commutative property of addition

(ii) Commutative property of multiplication

(iii) Associative property of addition

(iv) Associative property of multiplication

(v) Distributive property of multiplication over addition