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# 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