Chapter 7: Algebraic Expressions Exercise – 7.1

Question: 1

Identify the monomials, binomials, trinomials and quadrinomials from the following expressions:

(i) a²

(ii) a² − b²

(iii) x³ + y³ + z³

(iv) x³ + y³ + z³ + 3xyz

(v) 7 + 5

(vi) abc + 1

(vii) 3x – 2 + 5

(viii) 2x – 3y + 4

(ix) xy + yz + zx

(x) ax³ + bx² + cx + d

Solution:

The monomials, binomials, trinomials and quadrinomials are as follows.

(i) a² is a monomial expression as it contains one term only.

(ii) a² − b² is a binomial expression as it contains two terms.

(iii) x³ + y³ + z³ is a trinomial expression as it contains three terms.

(iv) x³ + y³ + z³ + 3xyz is a quadrinomial expression as it contains four terms.

(v) 7 + 5 = 12 is a monomial expression as it contains one term only.

(vi) abc + 1 is a binomial expression as it contains two terms.

(vii) 3x – 2 + 5 = 3x + 3 is a binomial expression as it contains two terms.

(viii) 2x – 3y + 4 is a trinomial expression as it contains three terms.

(ix) xy + yz + zx is a trinomial expression as it contains three terms.

(x) ax³ + bx² + cx + d is a quadrinomial expression as it contains four terms.

Question: 2

Write all the terms of each of the following algebraic expressions:

(i) 3x

(ii) 2x – 3

(iii) 2x² − 7

(iv) 2x² + y² − 3xy + 4

Solution:

The terms of each of the given algebraic expressions are as follows.

(i) 3x is the only term of the given algebraic expression.

(ii) 2x and -3 are the terms of the given algebraic expression.

(iii) 2x² and −7 are the terms of the given algebraic expression.

(iv) 2x², y², −3xy and 4 are the terms of the given algebraic expression.

Question: 3

Identify the terms and also mention the numerical coefficients of those terms:

(i) 4xy, -5x²y, -3yx, 2xy²

(ii) 7a²bc,-3ca²b,-(5/2) abc², 3/2abc²,-4/3cba²

Solution:

(i) Like terms - 4xy, -3yx and Numerical coefficients - 4, -3

(i) Like terms - {7a²bc, −3ca²b} and Numerical coefficients - 7, -3

{−5/2abc²}   {−5/2}

{3/2 abc²}     {3/2}

{−4/3cba²}    {−4/3}

Question: 4

Identify the like terms in the following algebraic expressions:

(i) a² + b² -2a² + c² + 4a

(ii) 3x + 4xy − 2yz + 52zy

(iii) abc + ab²c + 2acb² + 3c²ab + b²ac − 2a²bc + 3cab²

Solution:

The like terms in the given algebraic expressions are as follows.

(i) The like terms in the given algebraic expressions are a² and −2a².

(ii) The like terms in the given algebraic expressions are -2yz and 5/2zy.

(iii) The like terms in the given algebraic expressions are ab²c, 2acb², b²ac and 3cab².

Question: 5

Write the coefficient of x in the following:

(i) –12x

(ii) –7xy

(iii) xyz

(iv) –7ax

Solution:

The coefficients of x are as follows.

(i) The numerical coefficient of x is -12.

(ii) The numerical coefficient of x is -7y.

(iii) The numerical coefficient of x is yz.

(iv) The numerical coefficient of x is -7a.

Question: 6

Write the coefficient of 2 in the following:

(i) −3x²

(ii) 5x²yz

(iii) 5/7x²z

(iv) –(3/2) ax² + yx

Solution:

The coefficient of x² are as follows.

(i) The numerical coefficient of x² is -3.

(ii) The numerical coefficient of x² is 5yz.

(iii) The numerical coefficient of x² is 57z.

(iv) The numerical coefficient of x² is – (3/2) a.

Question: 7

Write the coefficient of:

(i) y in –3y

(ii) a in 2ab

(iii) z in –7xyz

(iv) p in –3pqr

(v) y² in 9xy²z

(vi) x³ in x³ +1

(vii) x² in − x²

Solution:

The coefficients are as follows.

(i) The coefficient of y is -3.

(ii) The coefficient of a is 2b.

(iii) The coefficient of z is -7xy.

(iv) The coefficient of p is -3qr.

(v) The coefficient of y² is 9xz.

(vi) The coefficient of x³ is 1.

(vii) The coefficient of −x² is -1.

Question: 8

Write the numerical coefficient of each in the following

(i) xy

(ii) -6yz

(iii) 7abc

(iv) -2x3y2z

Solution:

The numerical coefficient of each of the given terms is as follows.

(i) The numerical coefficient in the term xy is 1.

(ii) The numerical coefficient in the term - 6yz is - 6.

(iii) The numerical coefficient in the term 7abc is 7.

(iv) The numerical coefficient in the term −2x³y²z is -2.

Question: 9

Write the numerical coefficient of each term in the following algebraic expressions:

(i) 4x²y – (3/2)xy + 5/2 xy²

(ii) –(5/3)x²y + (7/4)xyz + 3

Solution:

The numerical coefficient of each term in the given algebraic expression is as follows.

Question: 10

Write the constant term of each of the following algebraic expressions:

(i) x²y − xy² + 7xy − 3

(ii) a³ − 3a² + 7a + 5

Solution:

The constant term of each of the given algebraic expressions is as follows.

(i) The constant term in the given algebraic expressions is -3.

(ii) The constant term in the given algebraic expressions is 5.

Question: 11

Evaluate each of the following expressions for x = -2, y = -1, z = 3:

Solution:

Question: 12

Evaluate each of the following algebraic expressions for x = 1, y = -1, z = 2, a = -2, b = 1, c = -2:

(i) ax + by + cz

(ii) ax² + by² – cz

(iii) axy + byz + cxy

Solution:

We have x = 1, y = -1, z = 2, a = -2, b = 1 and c = -2.

Thus,

(i) ax + by + cz

= (-2)(1) + (1)(-1) + (-2)(2)

= –2 – 1 – 4

= –7

(ii) ax² + by² – cz

= (-2) × 1² + 1 × (-1)² – (-2) × 2

= 4 + 1 – (-4)

= 5 + 4

= 9

(iii) axy + byz + cxy

= (-2) × 1 × -1 + 1 × -1 × 2 + (-2) × 1 × (-1)

= 2 + (-2) + 2

= 4 – 2

= 2