BINOMIALS WORKSHEET

Problem 1-5 : Add the binomials.

Problem 1 :

(3a + 2b) and (2a - 3b)

Problem 2 :

(7p²q + 5) and (2 - 5p²q)

Problem 3 :

(5xy - 2) and (2x - 4xy)

Problem 4 :

(x² + 2x²y) and (3xy² - x²)

Problem 5 :

(3a² + 2ab²), (2a² - 7a²b) and (4ab² - 3a²b)

Problem 6 :

Subtract (x + 2y) from (2x + y).

Problem 7 :

Subtract (7a - 8ab) from (3 - 5ab).

Problem 8 :

Subtract (5 - 6xy²) from (3 - 2xy²).

Problem 9 :

Subtract (5x²y - 7x²) from (7x² - 2x²y). 

Problem 10 :

Simplify :

(2p² + 5pq²) - (p² - 3p²q) - (9pq² - 5p²q)

Problem 11-12 : Multiply the binomials using Distributive Property.

Problem 11 : 

(x + 5) and (x - 7)

Problem 12 : 

(2x + 3y) and (3x - 2y)

Example 13 : 

Expand (p + q)² using Distributive Property.

Problem 14-15 : Multiply the binomials using FOIL method.

Example 14 : 

(x - 9) and (x + 13)

Example 15 : 

(7x² - 3y) and (3y + 2x²)

Example 16 : 

Expand (x - 5)² using FOIL method.

Answers

1. Answer :

= (3a + 2b) + (2a - 3b)

= 3a + 2b + 2a - 3b

Group the like terms and combine them.

= (3a + 2a) + (2b - 3b)

= 5a + (-b)

= 5a - b

2. Answer :

= (7p²q + 5) + (2 - 5p²q)

= 7p²q + 5 + 2 - 5p²q

Group the like terms and combine them.

= (7p²q - 5p²q) + (5 + 2)

= 2p²q + 7

3. Answer :

= (5xy - 2) + (2x - 4xy)

= 5xy - 2 + 2x - 4xy

Group the like terms and combine them.

= (5xy - 4xy) + 2x - 2

= xy + 2x - 2

4. Answer :

= (x² + 2x²y) + (3xy² - x²)

= x² + 2x²y + 3xy² - x²

Group the like terms and combine them.

= (x² - x²) + 2x²y + 3xy²

= 0 + 2x²y + 3xy²

= 2x²y + 3xy²

5. Answer :

= (3a² + 2ab²) + (2a² - 7a²b) + (4ab² - 3a²b)

= 3a² + 2ab² + 2a² - 7a²b + 4ab² - 3a²b

Group the like terms and combine them.

= (3a² + 2a²) + (-7a²b - 3a²b) + (2ab² + 4ab²)

= 5a² + (-10a²b) + 6ab²

= 5a² - 10a²b + 6ab²

6. Answer :

= (2x + y) - (x + 2y)

Distribute the negative sign.

= 2x + y - x - 2y

Combine the like terms by grouping.

= (2x - x) + (y - 2y)

= x + (-y)

= x - y

7. Answer :

= (3 - 5ab) - (7a - 8ab)

Distribute the negative sign.

= 3 - 5ab - 7a + 8ab

Combine the like terms by grouping.

= (-5ab + 8ab) - 7a + 3

= 3ab - 7a + 3

8. Answer :

= (3 - 2xy²) - (5 - 6xy²)

Distribute the negative sign.

= 3 - 2xy² - 5 + 6xy²

Combine the like terms by grouping.

= (-2xy² + 6xy²) + (3 - 5)

= 4xy² + (-2)

= 4xy² - 2

9. Answer :

= (7x² - 2x²y) - (5x²y - 7x²)

Distribute the negative sign.

= 7x² - 2x²y - 5x²y + 7x²

Combine the like terms by grouping.

= (7x² + 7x²) + (-2x²y - 5x²y)

= 14x² + (-7x²y)

= 14x² - 7x²y

10. Answer :

(2p² + 5pq²) - (p² - 3p²q) - (9pq² - 5p²q)

Distribute the negative signs.

= 2p² + 5pq² - p² + 3p²q - 9pq² + 5p²q

Group the like terms and combine them.

= (2p² - p²) + (3p²q + 5p²q) + (5pq² - 9pq²)

= p² + 8p²q + (-4pq²)

= p² + 8p²q - 4pq²

11. Answer :

= (x + 5)(x - 7)

Distribute. 

= x(x - 7) + 5(x - 7)

Distribute again. 

= x² - 7x + 5x - 35

Combine the like terms.

= x² - 2x - 35

12. Answer :

= (2x + 3y)(3x - 2y)

Distribute. 

= 2x(3x - 2y) + 3y(3x - 2y)

Distribute again. 

= 6x² - 4xy + 9xy - 6y²

Combine the like terms.

= 6x² + 5xy - 6y²

13. Answer :

= (p + q)²

Write as a product of two binomials.

= (p + q)(p + q)

Distribute.

= p(p + q) + q(p + q)

Distribute again. 

= p² + pq + pq + q²

Combine the like terms.

=  p² + 2pq + q²

14. Answer :

= (x - 9)(x + 13)

Use the FOIL method and multiply. 

= (x ⋅ x) + (x ⋅ 13) + (-9 ⋅ x) + (-9 ⋅ 13)

Multiply.

= x² + 13x + (-9x) + (-117)

= x² + 13x - 9x - 117

Combine the like terms. 

= x² + 4x - 117

15. Answer :

= (7x² - 3y)(3y + 2x²)

Use the FOIL method and multiply. 

= (7x² ⋅ 3y) + (7x²⋅ 2x²) + (-3y ⋅ 3y) + (-3y ⋅ 2x²)

Multiply.

= 21x²y + 14x⁴ + (-6y²) + (-6x²y)

= 21x²y + 14x⁴ - 6y² - 6x²y

Combine the like terms. 

= 14x⁴ + 15x²y - 6y²

16. Answer :

= (x - 5)²

Write as a product of two binomials. 

= (x - 5)(x - 5)

Use the FOIL method and multiply. 

= (x ⋅ x) + (x ⋅ -5) + (-5 ⋅ x) + (-5 ⋅ -5)

Multiply. 

= x² + (-5x) + (-5x) + 25

= x² - 5x - 5x + 25

Combine like terms. 

= x² - 10x + 25

Practice Questions

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