Parents and Teachers can provide their kids with extra practice and help them master the skill of multiplying a monomial with a binomial. You can solve complex math expressions quite easily if you know the concept of Multiplying Monomial and Binomial. In the Worksheet on Multiplying Monomial and Binomial, we have solved the questions by simply multiplying monomial with every individual term of the binomial and then further simplified.

Answer the problems in the Multiplying Monomial and Binomial Worksheet PDF and gain proficiency in the multiplication of monomial and a binomial. Multiplication of Monomial and Binomial Worksheet with Answers and improve your problem-solving ability with the interactive exercises provided.

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### Multiplying a Monomial by a Binomial Practice Worksheet

1. Multiply a monomial by a binomial
(i) 5ab × (3ab + 4)
(ii) (-2y2) × (x + y2)

Solution:

(i) Given, 5ab × (3ab + 4)
Step 1: Multiply the monomial with the first term of the binomial.
=5ab × (3ab) =15a2b2
Step 2: Multiply the monomial with the second term of the binomial.
=4(5ab)=20ab
Step 3: Write both the terms obtained in step 1 and step 2 together with their corresponding signs.
=15a2b2 + 20ab
Hence, By multiplying 5ab, (3ab + 4) we get 15a2b2+20ab.
(ii) Given, (-2y2) × (x + y2)
Step 1: Multiply the monomial with the first term of the binomial.
=(-2y2) × x =-2xy2
Step 2: Multiply the monomial with the second term of the binomial.
=(-2y2) × y2=-2y4
Step 3: Write both the terms obtained in step 1 and step 2 together with their corresponding signs.
=-2xy2-2y4
Hence, By multiplying (-2y2), (x + y2) we get -2xy2-2y4.

2. Find the Multiplication Result of a Monomial and a Binomial
(i) 5a2b3 × (a + b)
(ii) (-5x2) × (-2x2+8y)
(iii) (-4m) × (2m3 + m2n)

Solution:

(i) Given, 5a2b3 × (a + b)
Step 1: Multiply the monomial with the first term of the binomial.
=5a2b3 × (a)=5a3b3
Step 2: Multiply the monomial with the second term of the binomial.
= 5a2b3 × (b)=5a2b4
Step 3: Write both the terms obtained in step 1 and step 2 together with their corresponding signs.
=5a3b3+5a2b4
Hence, By multiplying 5a2b3, (a + b) we get 5a3b3+5a2b4.
(ii) Given, (-5x2) × (-2x2+8y)
Step 1: Multiply the monomial with the first term of the binomial.
=(-5x2) × (-2x2)=10x4
Step 2: Multiply the monomial with the second term of the binomial.
= (-5x2) × 8y=- 40x2y
Step 3: Write both the terms obtained in step 1 and step 2 together with their corresponding signs.
=10x4 – 40x2y
Hence, By multiplying (-5x2), (-2x2+8y) we get 10x4 – 40x2y.
(iii) Given, (-4m) × (2m3 + m2n)
Step 1: Multiply the monomial with the first term of the binomial.
=(-4m) × (2m3)=-8m4
Step 2: Multiply the monomial with the second term of the binomial.
=(-4m) × (m2n)=-4m3n
Step 3: Write both the terms obtained in step 1 and step 2 together with their corresponding signs.
=-8m4-4m3n
Hence, By multiplying (-4m) × (2m3 + m2n) we get -8m4-4m3n.

3. Multiply a binomial by a monomial:
(i) (6a + 2b) by ab2
(ii) (4m2n – 3m2) by 2mn

Solution:

(i) Given, (6a + 2b) by ab2
Step 1: Multiply the monomial with the first term of the binomial.
=6a × (ab2)=6a2b2
Step 2: Multiply the monomial with the second term of the binomial.
= 2b × (ab2)=2ab3
Step 3: Write both the terms obtained in step 1 and step 2 together with their corresponding signs.
=6a2b2+2ab3
Hence, By multiplying 6a + 2b, ab2 we get 6a2b2+2ab3.
(ii) Given, (4m2n – 3m2) by 2mn
Step 1: Multiply the monomial with the first term of the binomial.
=2mn × (4m2n)=8m3n2
Step 2: Multiply the monomial with the second term of the binomial.
-(3m2) × 2mn=-6m3n
Step 3: Write both the terms obtained in step 1 and step 2 together with their corresponding signs.
=8m3n2-6m3n
Hence, By multiplying 4m2n – 3m2,2mn we get 8m3n2-6m3n.

4. Multiply the following monomial with a binomial

(i) (5xy + 2y) by 2x2y2
(ii) (2b2 + 6c) by 5bc
(iii) (2mn + 5mp) by mnp

Solution:

(i) Given, (5xy + 2y) by 2x2y2
Step 1: Multiply the monomial with the first term of the binomial.
=5xy × (2x2y2)=10x3y3
Step 2: Multiply the monomial with the second term of the binomial.
=2y(2x2y2)=4x2y3
Step 3: Write both the terms obtained in step 1 and step 2 together with their corresponding signs.
=10x3y3+4x2y3
Hence, By multiplying 5xy + 2y,2x2y2 we get 10x3y3+4x2y3.
(ii) Given, (2b2 + 6c) by 5bc
Step 1: Multiply the monomial with the first term of the binomial.
=5bc(2b2 )=10b3c
Step 2: Multiply the monomial with the second term of the binomial.
=6c(5bc)=30bc2
Step 3: Write both the terms obtained in step 1 and step 2 together with their corresponding signs.
=10b3c + 30bc2
Hence, By multiplying 2b2 + 6c, 5bc we get 10b3c + 30bc2.
(iii) Given, (2mn + 5mp) by mnp
Step 1: Multiply the monomial with the first term of the binomial.
=mnp(2mn) =2m2n2p
Step 2: Multiply the monomial with the second term of the binomial.
= mnp(5mp)=5m2np2
Step 3: Write both the terms obtained in step 1 and step 2 together with their corresponding signs.
=2m2n2p + 5m2np2
Hence, By multiplying 2mn + 5mp, mnp we get 2m2n2p + 5m2np2.

5. Find the product of the following algebraic expressions
(i) 3b(12a + b4)
(ii) (-a2) (5 – 4a2)
(iii) 3x2(4x + 2y)

Solution:

(i) Given, 3b(12a + b4)
Multiply the monomial with the first term, the second term of the binomial and write both terms obtained with their corresponding signs.
=3b(12a) + 3b(b4)
=36ab + 3b5
Hence, the product of 3b, 12a + b4 we get 36ab + 3b5.
(ii) Given, (-a2) (5 – 4a2)
Multiply the monomial with the first term, the second term of the binomial and write both terms obtained with their corresponding signs.
=(-a2)(5) – (4a2)(-a2)
=-5a2 + 4a4
Hence, the product of (-a2), (5 – 4a2) we get -5a2 + 4a4.
(iii) Given, 3x2(4x + 2y)
Multiply the monomial with the first term, the second term of the binomial and write both terms obtained with their corresponding signs.
=3x2(4x) + 3x2(2y)
=12x3+6x2y
Hence, the product of 3x2(4x + 2y) we get 12x3+6x2y.

6. Find the product of the following monomial and binomial
(i) x2y(x2 + y2z)
(ii) (-12abc) (3ab + 4bc)

Solution:

(i) Given, x2y(x2 + y2z)
Multiply the monomial with the first term, the second term of the binomial and write both terms obtained with their corresponding signs.
=x2y(x2) + x2y(y2z)
=x4y + x2y3
Hence, the product of x2y,(x2 + y2z) we get x4y + x2y3.
(v) Given, (-12abc) (3ab + 4bc)
Multiply the monomial with the first term, the second term of the binomial and write both terms obtained with their corresponding signs.
=(-12abc) (3ab) + (-12abc)(4bc)
=-36a2b2c + (-48ab2c2)
= -36a2b2c -48ab2c2
Hence, the product of (-12abc) (3ab + 4bc) we get -36a2b2c -48ab2c2