Multiplying Polynomials Worksheet (original) (raw)

Last Updated : 23 Jul, 2025

A **polynomial is an algebraic expression consisting of variables and coefficients. We can perform various operations on polynomials, including **addition, subtraction, multiplication, and division. This worksheet focuses on **multiplying polynomials using different methods.

**Read More: Multiplying Polynomials

**Practice Questions on Polynomial Multiplication

Below are some solved examples:

**Question 1: Evaluate 100pq × 4qr × 8pr

**Solution:

Given: 100pq × 4qr × 8pr

So, we shall first multiply 100 pq and 4qr = 400pq2r

Now multiply this product with 8pr

Final product is 400pq2r × 8pr = 3200p2q2r2

We can obtain the same solution by first multiplying the coefficients 100 × 4 × 8 = 3200

The product of algebraic coefficients is pq × qr × pr = p2q2r2

So, the final product is 3200p2q2r2

**Question 2: Find 5pqr × 10 rst

**Solution:

Multiply the coefficients 5 × 10 =50
Multiply the algebraic coefficients = pqr × rst = pqr2st

So, Product = 50pqr2st
The result of multiplication doesn't depend on the order in which multiplication is carried out.

**Question 3: Multiply 20m × (10n + 3).

**Solution:

Given: 20m x (10n + 3)

Using the distributive laws,
= (20m × 10n) + (20m × 3)
= 200mn + 60m

**Question 4: Find the product 19p × (2q + 3z + 5pq)

**Solution:

Given: 19p × (2q + 3z + 5pq)

Using the distributive law,
= (19p × 2q) + (19p × 3z) + (19p × 5pq)
= 38pq + 57pz + 95p2q

**Question 5: Multiply (2x - 4y) and (3x - 5y).

**Solution:

Given: (2x - 4y) × (3x - 5y)

Using the distributive laws,
[2x × (3x - 5y)] - [4y × (3x - 5y)]
[6x2 - 10xy] - [12xy - 20y2]
6x2 - 10xy - 12xy - 20y2
6x2 - 20y2 - 22xy

**Question 6: Multiply (2x + 4y) and (2x + y).

**Solution:

Given: (2x + 4y) × (2x + y)

Using the distributive laws,
[2x × (2x + y)] + [4y × (2x + y)]
[4x2 + 2xy] + [8xy + 4y2]
4x2 + 2xy + 8xy + 4y2
4x2 + 4y2 + 10xy

**Question 7: Find the value of 3m (4m - 5) + 4 when m = 1

**Solution

Given: 3m (4m - 5) + 4, m = 1
3m(4m - 5) = 12m2 - 15m

So, 3m (4m - 5) + 4 = 12m2 - 15m + 4

Now put the value m = 1
= 12(1)2 - 15 (1) + 4
= 12 - 15 + 4
= 1

**Question 8: Multiply (t - 5) and (3m + 5)

**Solution:

Given: (t - 5) × (3m + 5)

Using distributed law
t(3m + 5) - 5(3m + 5)
3tm + 5t - 15m - 25

**Question 9: Multiply (z + 4) and (z - 4)

**Solution:

Given: (z + 4) × (z - 4)

Using distributed law
= z(z - 4) + 4(z - 4)
= z2 - 4z + 4z - 16
= z2 - 16

**Question 10: Multiply (m - n) and (3m + 5n)

**Solution:

Given: (m - n) × (3m + 5n)

Using distributed law
= m(3m + 5n) - n(3m + 5n)
= 3m2 + 5mn - 3mn - 5n2
= 3m2 + 2mn - 5n2

**Question 11: Simplify (m - n)(2m + 3n + r)

**Solution:

Given: (m - n)(2m + 3n + r)

Using distributed law
= m(2m + 3n + r) - n(2m + 3n + r)
= 2m2 + 3mn + mr - 2mn - 3n2 - nr
= 2m2 + mn - 3n2 + mr - nr

**Question 12: Evaluate (p + q) (p + q + r)

**Solution:

Given: (p + q)(p + q + r)

Using distributed law
= p(p + q + r) + q(p + q + r)
= p2 + pq + pr + pq + q2 + qr
= p2 + q2 + 2pq + pr + qr

**Question 13: Evaluate (4 + 5t)(5 + 3t + q)

**Solution

Given: (4 + 5t)(5 + 3t + q)

Using distributed law
= 4(5 + 3t + q) + 5t (5 + 3t + q)
= 20 + 12t + 4q + 25t + 15 t2 + 5tq
= 15t2 + 37t + 5tq + 4q + 20

**Unsolved Practice Questions on Polynomial Mulitplication

  1. Multiply 7xy × 3yz × 2xz
  2. Find the product of 5pqr × 8rst
  3. Multiply 15m × (7n + 4)
  4. Find the product of 12a × (4b + 2c + 6ab)
  5. Multiply (3x + 5y) and (2x − 4y)
  6. Multiply (4x + 2y) and (3x − y)
  7. Find the value of 2m(3m − 4) + 5 when = 2
  8. Multiply (x−6) and (4y + 3)

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