# 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)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)using FOIL method.

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

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

Group the like terms and combine them.

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

= 5a + (-b)

= 5a - b

= (7p2q + 5) + (2 - 5p2q)

= 7p2q + 5 + 2 - 5p2q

Group the like terms and combine them.

= (7p2q - 5p2q) + (5 + 2)

= 2p2q + 7

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

= 5xy - 2 + 2x - 4xy

Group the like terms and combine them.

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

= xy + 2x - 2

= (x2 + 2x2y) + (3xy2 - x2)

= x2 + 2x2y + 3xy2 - x2

Group the like terms and combine them.

= (x2 - x2+ 2x2y + 3xy2

= 0 + 2x2y + 3xy2

= 2x2y + 3xy2

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

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

Group the like terms and combine them.

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

= 5a2 + (-10a2b) + 6ab2

= 5a2 - 10a2b + 6ab2

= (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

= (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

= (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

= (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

(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

= (x + 5)(x - 7)

Distribute.

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

Distribute again.

= x2 - 7x + 5x - 35

Combine the like terms.

= x2 - 2x - 35

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

Distribute.

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

Distribute again.

= 6x2 - 4xy + 9xy - 6y2

Combine the like terms.

= 6x2 + 5xy - 6y2

(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

= (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

= (7x2 - 3y)(3y + 2x2)

Use the FOIL method and multiply.

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

Multiply.

= 21x2y + 14x4 + (-6y2) + (-6x2y)

= 21x2y + 14x4 - 6y2 - 6x2y

Combine the like terms.

= 14x4 + 15x2y - 6y2

= (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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