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