Algebraic Expressions (Exercise 7.1) RD Sharma Solutions | Mathematics (Maths) Class 7 PDF Download

 Page 1


 
 
 
 
 
 
 
Exercise 7.1         Page No: 7.7 
 
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) a b c + 1 
(vii) 3x – 2 + 5 
(viii) 2x – 3y + 4 
(ix) x y + y z + z x 
(x) ax
3
 + bx
2
 + cx + d 
 
Solution: 
(i) Given a
2
 
a
2
 is a monomial expression because it contains only one term 
 
(ii) Given a
2
 - b
2 
a
2 
- b
2
 is a binomial expression because it contains two terms 
 
(iii) Given x
3
 + y
3
 + z
3
 
x
3
 + y
3
 + z
3
 is a trinomial because it contains three terms 
 
(iv) Given x
3 
+ y
3 
+ z
3
 + 3xyz 
x
3
 + y
3 
+ z
3
 + 3xyz is a quadrinomial expression because it contains four terms 
 
(v) Given 7 + 5 
7 + 5 is a monomial expression because it contains only one term 
 
(vi) Given a b c + 1 
a b c + 1 is a binomial expression because it contains two terms 
 
(vii) Given 3x – 2 + 5 
3x – 2 + 5 is a binomial expression because it contains two terms 
Page 2


 
 
 
 
 
 
 
Exercise 7.1         Page No: 7.7 
 
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) a b c + 1 
(vii) 3x – 2 + 5 
(viii) 2x – 3y + 4 
(ix) x y + y z + z x 
(x) ax
3
 + bx
2
 + cx + d 
 
Solution: 
(i) Given a
2
 
a
2
 is a monomial expression because it contains only one term 
 
(ii) Given a
2
 - b
2 
a
2 
- b
2
 is a binomial expression because it contains two terms 
 
(iii) Given x
3
 + y
3
 + z
3
 
x
3
 + y
3
 + z
3
 is a trinomial because it contains three terms 
 
(iv) Given x
3 
+ y
3 
+ z
3
 + 3xyz 
x
3
 + y
3 
+ z
3
 + 3xyz is a quadrinomial expression because it contains four terms 
 
(v) Given 7 + 5 
7 + 5 is a monomial expression because it contains only one term 
 
(vi) Given a b c + 1 
a b c + 1 is a binomial expression because it contains two terms 
 
(vii) Given 3x – 2 + 5 
3x – 2 + 5 is a binomial expression because it contains two terms 
 
 
(viii) Given 2x – 3y + 4
2x – 3y + 4 is a trinomial because it contains three terms
(ix) Given x y + y z + z x
x y + y z + z x is a trinomial because it contains three terms
(x) Given ax
3
 + bx
2
 + cx + d
ax
3
 + bx
2
 + cx + d is a quadrinomial expression because it contains four terms
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: 
(i) Given 3x
3x is the only term of the given algebraic expression.
(ii) Given 2x – 3
2x and -3 are the terms of the given algebraic expression.
(iii) Given 2x
2
 - 7
2x
2
 and -7 are the terms of the given algebraic expression.
(iv) Given 2x
2 
+ y
2 
- 3xy + 4
2x
2
, y
2
, -3xy and 4 are the terms of the given algebraic expression.
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
,(-4/3)cba
2
Solution: 
(i) Like terms 4xy, -3yx and Numerical coefficients 4, -3
(ii) Like terms (-7a
2
bc, -3ca
2
b) and (-4/3cba
2
) and their Numerical coefficients 7, -3,
(-4/3)
Page 3


 
 
 
 
 
 
 
Exercise 7.1         Page No: 7.7 
 
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) a b c + 1 
(vii) 3x – 2 + 5 
(viii) 2x – 3y + 4 
(ix) x y + y z + z x 
(x) ax
3
 + bx
2
 + cx + d 
 
Solution: 
(i) Given a
2
 
a
2
 is a monomial expression because it contains only one term 
 
(ii) Given a
2
 - b
2 
a
2 
- b
2
 is a binomial expression because it contains two terms 
 
(iii) Given x
3
 + y
3
 + z
3
 
x
3
 + y
3
 + z
3
 is a trinomial because it contains three terms 
 
(iv) Given x
3 
+ y
3 
+ z
3
 + 3xyz 
x
3
 + y
3 
+ z
3
 + 3xyz is a quadrinomial expression because it contains four terms 
 
(v) Given 7 + 5 
7 + 5 is a monomial expression because it contains only one term 
 
(vi) Given a b c + 1 
a b c + 1 is a binomial expression because it contains two terms 
 
(vii) Given 3x – 2 + 5 
3x – 2 + 5 is a binomial expression because it contains two terms 
 
 
(viii) Given 2x – 3y + 4
2x – 3y + 4 is a trinomial because it contains three terms
(ix) Given x y + y z + z x
x y + y z + z x is a trinomial because it contains three terms
(x) Given ax
3
 + bx
2
 + cx + d
ax
3
 + bx
2
 + cx + d is a quadrinomial expression because it contains four terms
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: 
(i) Given 3x
3x is the only term of the given algebraic expression.
(ii) Given 2x – 3
2x and -3 are the terms of the given algebraic expression.
(iii) Given 2x
2
 - 7
2x
2
 and -7 are the terms of the given algebraic expression.
(iv) Given 2x
2 
+ y
2 
- 3xy + 4
2x
2
, y
2
, -3xy and 4 are the terms of the given algebraic expression.
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
,(-4/3)cba
2
Solution: 
(i) Like terms 4xy, -3yx and Numerical coefficients 4, -3
(ii) Like terms (-7a
2
bc, -3ca
2
b) and (-4/3cba
2
) and their Numerical coefficients 7, -3,
(-4/3)
 
 
Like terms are (-5/2abc
2
) and (3/2 abc
2
) and numerical coefficients are (-5/2) and (3/2) 
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: 
(i) Given a
2
 + b
2 
-2a
2
 + c
2
 + 4a
The like terms in the given algebraic expressions are a
2
 and -2a
2
.
(ii) Given 3x + 4xy - 2yz + 52zy
The like terms in the given algebraic expressions are -2yz and 52zy.
(iii) Given abc + ab
2
c + 2acb
2 
+ 3c
2
ab + b
2
ac - 2a
2
bc + 3cab
2
The like terms in the given algebraic expressions are ab
2
c, 2acb
2
, b
2
ac and 3cab
2
.
5. Write the coefficient of x in the following:
(i) –12x
(ii) –7xy
(iii) xyz
(iv) –7ax
Solution: 
(i) Given -12x
The numerical coefficient of x is -12.
(ii) Given -7xy
The numerical coefficient of x is -7y.
(iii) Given xyz
The numerical coefficient of x is yz.
(iv) Given -7ax
The numerical coefficient of x is -7a.
6. Write the coefficient of x
2
 in the following:
Page 4


 
 
 
 
 
 
 
Exercise 7.1         Page No: 7.7 
 
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) a b c + 1 
(vii) 3x – 2 + 5 
(viii) 2x – 3y + 4 
(ix) x y + y z + z x 
(x) ax
3
 + bx
2
 + cx + d 
 
Solution: 
(i) Given a
2
 
a
2
 is a monomial expression because it contains only one term 
 
(ii) Given a
2
 - b
2 
a
2 
- b
2
 is a binomial expression because it contains two terms 
 
(iii) Given x
3
 + y
3
 + z
3
 
x
3
 + y
3
 + z
3
 is a trinomial because it contains three terms 
 
(iv) Given x
3 
+ y
3 
+ z
3
 + 3xyz 
x
3
 + y
3 
+ z
3
 + 3xyz is a quadrinomial expression because it contains four terms 
 
(v) Given 7 + 5 
7 + 5 is a monomial expression because it contains only one term 
 
(vi) Given a b c + 1 
a b c + 1 is a binomial expression because it contains two terms 
 
(vii) Given 3x – 2 + 5 
3x – 2 + 5 is a binomial expression because it contains two terms 
 
 
(viii) Given 2x – 3y + 4
2x – 3y + 4 is a trinomial because it contains three terms
(ix) Given x y + y z + z x
x y + y z + z x is a trinomial because it contains three terms
(x) Given ax
3
 + bx
2
 + cx + d
ax
3
 + bx
2
 + cx + d is a quadrinomial expression because it contains four terms
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: 
(i) Given 3x
3x is the only term of the given algebraic expression.
(ii) Given 2x – 3
2x and -3 are the terms of the given algebraic expression.
(iii) Given 2x
2
 - 7
2x
2
 and -7 are the terms of the given algebraic expression.
(iv) Given 2x
2 
+ y
2 
- 3xy + 4
2x
2
, y
2
, -3xy and 4 are the terms of the given algebraic expression.
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
,(-4/3)cba
2
Solution: 
(i) Like terms 4xy, -3yx and Numerical coefficients 4, -3
(ii) Like terms (-7a
2
bc, -3ca
2
b) and (-4/3cba
2
) and their Numerical coefficients 7, -3,
(-4/3)
 
 
Like terms are (-5/2abc
2
) and (3/2 abc
2
) and numerical coefficients are (-5/2) and (3/2) 
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: 
(i) Given a
2
 + b
2 
-2a
2
 + c
2
 + 4a
The like terms in the given algebraic expressions are a
2
 and -2a
2
.
(ii) Given 3x + 4xy - 2yz + 52zy
The like terms in the given algebraic expressions are -2yz and 52zy.
(iii) Given abc + ab
2
c + 2acb
2 
+ 3c
2
ab + b
2
ac - 2a
2
bc + 3cab
2
The like terms in the given algebraic expressions are ab
2
c, 2acb
2
, b
2
ac and 3cab
2
.
5. Write the coefficient of x in the following:
(i) –12x
(ii) –7xy
(iii) xyz
(iv) –7ax
Solution: 
(i) Given -12x
The numerical coefficient of x is -12.
(ii) Given -7xy
The numerical coefficient of x is -7y.
(iii) Given xyz
The numerical coefficient of x is yz.
(iv) Given -7ax
The numerical coefficient of x is -7a.
6. Write the coefficient of x
2
 in the following:
 
 
(i) -3x
2
(ii) 5x
2
yz
(iii) 5/7x
2
z
(iv) (-3/2) ax
2
 + yx
Solution: 
(i) Given -3x
2
The numerical coefficient of x
2
 is -3.
(ii) Given 5x
2
yz
The numerical coefficient of x
2
 is 5yz.
(iii) Given5/7x
2
z
The numerical coefficient of x
2
 is 5/7z.
(iv) Given (-3/2) ax
2
 + yx
The numerical coefficient of x
2
 is – (3/2) a.
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: 
(i) Given –3y
The coefficient of y is -3.
(ii) Given 2ab
The coefficient of a is 2b.
(iii) Given -7xyz
The coefficient of z is -7xy.
Page 5


 
 
 
 
 
 
 
Exercise 7.1         Page No: 7.7 
 
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) a b c + 1 
(vii) 3x – 2 + 5 
(viii) 2x – 3y + 4 
(ix) x y + y z + z x 
(x) ax
3
 + bx
2
 + cx + d 
 
Solution: 
(i) Given a
2
 
a
2
 is a monomial expression because it contains only one term 
 
(ii) Given a
2
 - b
2 
a
2 
- b
2
 is a binomial expression because it contains two terms 
 
(iii) Given x
3
 + y
3
 + z
3
 
x
3
 + y
3
 + z
3
 is a trinomial because it contains three terms 
 
(iv) Given x
3 
+ y
3 
+ z
3
 + 3xyz 
x
3
 + y
3 
+ z
3
 + 3xyz is a quadrinomial expression because it contains four terms 
 
(v) Given 7 + 5 
7 + 5 is a monomial expression because it contains only one term 
 
(vi) Given a b c + 1 
a b c + 1 is a binomial expression because it contains two terms 
 
(vii) Given 3x – 2 + 5 
3x – 2 + 5 is a binomial expression because it contains two terms 
 
 
(viii) Given 2x – 3y + 4
2x – 3y + 4 is a trinomial because it contains three terms
(ix) Given x y + y z + z x
x y + y z + z x is a trinomial because it contains three terms
(x) Given ax
3
 + bx
2
 + cx + d
ax
3
 + bx
2
 + cx + d is a quadrinomial expression because it contains four terms
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: 
(i) Given 3x
3x is the only term of the given algebraic expression.
(ii) Given 2x – 3
2x and -3 are the terms of the given algebraic expression.
(iii) Given 2x
2
 - 7
2x
2
 and -7 are the terms of the given algebraic expression.
(iv) Given 2x
2 
+ y
2 
- 3xy + 4
2x
2
, y
2
, -3xy and 4 are the terms of the given algebraic expression.
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
,(-4/3)cba
2
Solution: 
(i) Like terms 4xy, -3yx and Numerical coefficients 4, -3
(ii) Like terms (-7a
2
bc, -3ca
2
b) and (-4/3cba
2
) and their Numerical coefficients 7, -3,
(-4/3)
 
 
Like terms are (-5/2abc
2
) and (3/2 abc
2
) and numerical coefficients are (-5/2) and (3/2) 
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: 
(i) Given a
2
 + b
2 
-2a
2
 + c
2
 + 4a
The like terms in the given algebraic expressions are a
2
 and -2a
2
.
(ii) Given 3x + 4xy - 2yz + 52zy
The like terms in the given algebraic expressions are -2yz and 52zy.
(iii) Given abc + ab
2
c + 2acb
2 
+ 3c
2
ab + b
2
ac - 2a
2
bc + 3cab
2
The like terms in the given algebraic expressions are ab
2
c, 2acb
2
, b
2
ac and 3cab
2
.
5. Write the coefficient of x in the following:
(i) –12x
(ii) –7xy
(iii) xyz
(iv) –7ax
Solution: 
(i) Given -12x
The numerical coefficient of x is -12.
(ii) Given -7xy
The numerical coefficient of x is -7y.
(iii) Given xyz
The numerical coefficient of x is yz.
(iv) Given -7ax
The numerical coefficient of x is -7a.
6. Write the coefficient of x
2
 in the following:
 
 
(i) -3x
2
(ii) 5x
2
yz
(iii) 5/7x
2
z
(iv) (-3/2) ax
2
 + yx
Solution: 
(i) Given -3x
2
The numerical coefficient of x
2
 is -3.
(ii) Given 5x
2
yz
The numerical coefficient of x
2
 is 5yz.
(iii) Given5/7x
2
z
The numerical coefficient of x
2
 is 5/7z.
(iv) Given (-3/2) ax
2
 + yx
The numerical coefficient of x
2
 is – (3/2) a.
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: 
(i) Given –3y
The coefficient of y is -3.
(ii) Given 2ab
The coefficient of a is 2b.
(iii) Given -7xyz
The coefficient of z is -7xy.
 
 
(iv) Given -3pqr
The coefficient of p is -3qr.
(v) Given 9xy
2
z
The coefficient of y
2
 is 9xz.
(vi) Given x
3
 +1
The coefficient of x
3
 is 1.
(vii) Given - x
2
The coefficient of x
2
 is -1.
8. Write the numerical coefficient of each in the following:
(i) xy
(ii) -6yz
(iii) 7abc
(iv) -2x
3
y
2
z
Solution: 
(i) Given xy
The numerical coefficient in the term xy is 1.
(ii) Given -6yz
The numerical coefficient in the term - 6yz is - 6.
(iii) Given 7abc
The numerical coefficient in the term 7abc is 7.
(iv) Given -2x
3
y
2
z
The numerical coefficient in the term -2x
3
y
2
z is -2.
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: 
(i) Given 4x
2
y – (3/2) xy + 5/2 xy
2