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.

Do Refer:

- Worksheet on Multiplying Monomial and Polynomial
- Worksheet on Multiplying Binomials
- Worksheet on Dividing Monomials

### Multiplying a Monomial by a Binomial Practice Worksheet

1. Multiply a monomial by a binomial

(i) 5ab × (3ab + 4)

(ii) (-2y^{2}) × (x + y^{2})

**Solution:**

(i) Given, 5ab × (3ab + 4)

**Step 1:** Multiply the monomial with the first term of the binomial.

=5ab × (3ab) =15a^{2}b^{2 }

**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.

=15a^{2}b^{2} + 20ab

Hence, By multiplying 5ab, (3ab + 4) we get 15a^{2}b^{2}+20ab.

(ii) Given, (-2y^{2}) × (x + y^{2})

**Step 1:** Multiply the monomial with the first term of the binomial.

=(-2y^{2}) × x =-2xy^{2}

**Step 2:** Multiply the monomial with the second term of the binomial.

=(-2y^{2}) × y^{2}=-2y^{4}

**Step 3:** Write both the terms obtained in step 1 and step 2 together with their corresponding signs.

=-2xy^{2}-2y^{4}

Hence, By multiplying (-2y^{2}), (x + y^{2}) we get -2xy^{2}-2y^{4}.

2. Find the Multiplication Result of a Monomial and a Binomial

(i) 5a^{2}b^{3} × (a + b)

(ii) (-5x^{2}) × (-2x^{2}+8y)

(iii) (-4m) × (2m^{3} + m^{2}n)

**Solution:**

(i) Given, 5a2b3 × (a + b)

**Step 1: **Multiply the monomial with the first term of the binomial.

=5a^{2}b^{3} × (a)=5a^{3}b^{3}

**Step 2: **Multiply the monomial with the second term of the binomial.

= 5a^{2}b^{3} × (b)=5a^{2}b^{4}

**Step 3: **Write both the terms obtained in step 1 and step 2 together with their corresponding signs.

=5a^{3}b^{3}+5a^{2}b^{4}

Hence, By multiplying 5a^{2}b^{3}, (a + b) we get 5a^{3}b^{3}+5a^{2}b^{4}.

(ii) Given, (-5x^{2}) × (-2x^{2}+8y)

**Step 1:** Multiply the monomial with the first term of the binomial.

=(-5x^{2}) × (-2x^{2})=10x^{4}

**Step 2:** Multiply the monomial with the second term of the binomial.

= (-5x^{2}) × 8y=- 40x^{2}y

**Step 3:** Write both the terms obtained in step 1 and step 2 together with their corresponding signs.

=10x^{4} – 40x^{2}y

Hence, By multiplying (-5x^{2}), (-2x^{2}+8y) we get 10x^{4} – 40x^{2}y.

(iii) Given, (-4m) × (2m^{3} + m^{2}n)

**Step 1:** Multiply the monomial with the first term of the binomial.

=(-4m) × (2m^{3})=-8m^{4}

**Step 2:** Multiply the monomial with the second term of the binomial.

=(-4m) × (m^{2}n)=-4m^{3}n

**Step 3:** Write both the terms obtained in step 1 and step 2 together with their corresponding signs.

=-8m^{4}-4m^{3}n

Hence, By multiplying (-4m) × (2m^{3} + m^{2}n) we get -8m^{4}-4m^{3}n.

**3. Multiply a binomial by a monomial:
**(i) (6a + 2b) by ab

^{2}

(ii) (4m

^{2}n – 3m

^{2}) by 2mn

**Solution:**

(i) Given, (6a + 2b) by ab^{2}

**Step 1:** Multiply the monomial with the first term of the binomial.

=6a × (ab^{2})=6a^{2}b^{2}

**Step 2:** Multiply the monomial with the second term of the binomial.

= 2b × (ab^{2})=2ab^{3}

**Step 3:** Write both the terms obtained in step 1 and step 2 together with their corresponding signs.

=6a^{2}b^{2}+2ab^{3}

Hence, By multiplying 6a + 2b, ab^{2} we get 6a^{2}b^{2}+2ab^{3}.

(ii) Given, (4m^{2}n – 3m^{2}) by 2mn

**Step 1:** Multiply the monomial with the first term of the binomial.

=2mn × (4m^{2}n)=8m^{3}n^{2
}**Step 2:** Multiply the monomial with the second term of the binomial.

-(3m^{2}) × 2mn=-6m^{3}n

**Step 3:** Write both the terms obtained in step 1 and step 2 together with their corresponding signs.

=8m^{3}n^{2}-6m^{3}n

Hence, By multiplying 4m^{2}n – 3m^{2},2mn we get 8m^{3}n^{2}-6m^{3}n.

**4. Multiply the following monomial with a binomial**

(i) (5xy + 2y) by 2x^{2}y^{2}

(ii) (2b^{2} + 6c) by 5bc

(iii) (2mn + 5mp) by mnp

**Solution:**

(i) Given, (5xy + 2y) by 2x^{2}y^{2}

**Step 1:** Multiply the monomial with the first term of the binomial.

=5xy × (2x^{2}y^{2})=10x^{3}y^{3}

**Step 2:** Multiply the monomial with the second term of the binomial.

=2y(2x^{2}y^{2})=4x^{2}y^{3}

**Step 3:** Write both the terms obtained in step 1 and step 2 together with their corresponding signs.

=10x^{3}y^{3}+4x^{2}y^{3}

Hence, By multiplying 5xy + 2y,2x^{2}y^{2} we get 10x^{3}y^{3}+4x^{2}y^{3}.

(ii) Given, (2b^{2} + 6c) by 5bc

**Step 1:** Multiply the monomial with the first term of the binomial.

=5bc(2b^{2} )=10b^{3}c

**Step 2:** Multiply the monomial with the second term of the binomial.

=6c(5bc)=30bc^{2}

**Step 3:** Write both the terms obtained in step 1 and step 2 together with their corresponding signs.

=10b^{3}c + 30bc^{2}

Hence, By multiplying 2b^{2} + 6c, 5bc we get 10b^{3}c + 30bc^{2}.

(iii) Given, (2mn + 5mp) by mnp

**Step 1:** Multiply the monomial with the first term of the binomial.

=mnp(2mn) =2m^{2}n^{2}p

**Step 2:** Multiply the monomial with the second term of the binomial.

= mnp(5mp)=5m^{2}np^{2}

**Step 3:** Write both the terms obtained in step 1 and step 2 together with their corresponding signs.

=2m^{2}n^{2}p + 5m^{2}np^{2}

Hence, By multiplying 2mn + 5mp, mnp we get 2m^{2}n^{2}p + 5m^{2}np^{2}.

**5. Find the product of the following algebraic expressions
**(i) 3b(12a + b

^{4})

(ii) (-a

^{2}) (5 – 4a

^{2})

(iii) 3x

^{2}(4x + 2y)

**Solution:**

(i) Given, 3b(12a + b^{4})

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(b^{4})

=36ab + 3b^{5
}Hence, the product of 3b, 12a + b^{4} we get 36ab + 3b^{5}.

(ii) Given, (-a^{2}) (5 – 4a^{2})

Multiply the monomial with the first term, the second term of the binomial and write both terms obtained with their corresponding signs.

=(-a^{2})(5) – (4a^{2})(-a^{2})

=-5a^{2} + 4a^{4
}Hence, the product of (-a^{2}), (5 – 4a^{2}) we get -5a^{2} + 4a^{4.
}(iii) Given, 3x^{2}(4x + 2y)

Multiply the monomial with the first term, the second term of the binomial and write both terms obtained with their corresponding signs.

=3x^{2}(4x) + 3x^{2}(2y)

=12x^{3}+6x^{2}y

Hence, the product of 3x^{2}(4x + 2y) we get 12x^{3}+6x^{2}y.

**6. Find the product of the following monomial and binomial**

(i) x^{2}y(x^{2} + y^{2}z)

(ii) (-12abc) (3ab + 4bc)

**Solution:**

(i) Given, x^{2}y(x^{2} + y^{2}z)

Multiply the monomial with the first term, the second term of the binomial and write both terms obtained with their corresponding signs.

=x^{2}y(x^{2}) + x^{2}y(y^{2}z)

=x^{4}y + x^{2}y^{3}

Hence, the product of x^{2}y,(x^{2} + y^{2}z) we get x^{4}y + x^{2}y^{3}.

(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)

=-36a^{2}b^{2}c + (-48ab^{2}c^{2})

= -36a^{2}b^{2}c -48ab^{2}c^{2}

Hence, the product of (-12abc) (3ab + 4bc) we get -36a^{2}b^{2}c -48ab^{2}c^{2}