**Chapter 7: Algebraic Expressions Exercise – 7.1**

**Question: 1**

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

(i) a^{2}

(ii) a^{2} − b^{2}

(iii) x^{3} + y^{3} + z^{3}

(iv) x^{3 }+ y^{3 }+ z^{3} + 3xyz

(v) 7 + 5

(vi) abc + 1

(vii) 3x – 2 + 5

(viii) 2x – 3y + 4

(ix) xy + yz + zx

(x) ax^{3} + bx^{2} + cx + d

**Solution:**

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

(i) a^{2} is a monomial expression as it contains one term only.

(ii) a^{2 }− b^{2} is a binomial expression as it contains two terms.

(iii) x^{3} + y^{3} + z^{3} is a trinomial expression as it contains three terms.

(iv) x^{3} + y^{3 }+ z^{3} + 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) ax^{3} + bx^{2} + 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) 2x^{2} − 7

(iv) 2x^{2 }+ y^{2 }− 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) 2x^{2} and −7 are the terms of the given algebraic expression.

(iv) 2x^{2}, y^{2}, −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, -5x^{2}y, -3yx, 2xy^{2}

(ii) 7a^{2}bc,-3ca^{2}b,-(5/2) abc^{2}, 3/2abc^{2},-4/3cba^{2}

**Solution:**

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

(i) Like terms - {7a^{2}bc, −3ca^{2}b} and Numerical coefficients - 7, -3

{−5/2abc^{2}} {−5/2}

{3/2 abc^{2}} {3/2}

{−4/3cba^{2}} {−4/3}

**Question: 4**

Identify the like terms in the following algebraic expressions:

(i) a^{2} + b^{2 }-2a^{2} + c^{2} + 4a

(ii) 3x + 4xy − 2yz + 52zy

(iii) abc + ab^{2}c + 2acb^{2 }+ 3c^{2}ab + b^{2}ac − 2a^{2}bc + 3cab^{2}

**Solution:**

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

(i) The like terms in the given algebraic expressions are a^{2} and −2a^{2}.

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

(iii) The like terms in the given algebraic expressions are ab^{2}c, 2acb^{2}, b^{2}ac and 3cab^{2}.

**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) −3x^{2}

(ii) 5x^{2}yz

(iii) 5/7x^{2}z

(iv) –(3/2) ax^{2} + yx

**Solution:**

The coefficient of x^{2} are as follows.

(i) The numerical coefficient of x^{2} is -3.

(ii) The numerical coefficient of x^{2} is 5yz.

(iii) The numerical coefficient of x^{2} is 57z.

(iv) The numerical coefficient of x^{2} 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) y^{2} in 9xy^{2}z

(vi) x^{3} in x^{3} +1

(vii) x^{2} in − x^{2}

**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 y^{2} is 9xz.

(vi) The coefficient of x^{3} is 1.

(vii) The coefficient of −x^{2} 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 −2x^{3}y^{2}z is -2.

**Question: 9**

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

(i) 4x^{2}y – (3/2)xy + 5/2 xy^{2}

(ii) –(5/3)x^{2}y + (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) x^{2}y − xy^{2} + 7xy − 3

(ii) a^{3} − 3a^{2} + 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) ax^{2} + by^{2} – 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) ax^{2} + by^{2} – cz

= (-2) × 1^{2} + 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