Multiplying Binomials

Mrs. BookLiberty Hill Middle School

Algebra I

BellworkSimplify. Write the answer in

standard form.(x3 + 3x2 + x) + (5x2 + x + 1)m(4m2 – 6) + 3m2(m + 9)3d2(d3 – 6) – d3(2d2 + 4)

Multiplying Binomials

• Distributive Property Method–Vertical–Horizontal

• FOIL Method• Applying Multiplication of Binomials

Distributive Method

• Vertical Method• (2x + 3)(x + 5)

2x + 3(×) x + 510x + 15

2x2 + 3x + 10x + 15

Multiply by 5

Multiply by x2x2 + 3x

Distributive Method

• Horizontal Method• (2x + 3)(x + 5)• 2x (x + 5) + 3 (x + 5) Rewrite as the sum of two products

• Distribute• 2x2 + 10x + 3x + 15• 2x2 + 13x + 15

Combine like terms

FOIL Method

• To multiply two binomials find the sum of the products of F the First terms, O the Outer terms, I the Inner terms, and L the Last terms.

• ( 2x + 3 )( x + 5 )

• 2x2 + 13x + 152x2 + 10x + 3x + 15

Combine like terms

Find the Product

(3c – 5)(c + 3)

Find the Product

(12t – 5)(12t + 5)

Find the Product

(8w + 4x)(5w – 6x)

Applying Multiplication of Polynomials

Applying Multiplication of Polynomials

• You are planning a rectangular garden. Its length is twice its width x. You want a walkway 2 ft wide around the garden.

a. Write an expression for the area of the garden and walkb. Write an expression for the area of the

walk only.c. You have enough gravel to cover 76 ft2

and want to use it all on the walk. How big should you make the garden?

Applying Multiplication of Polynomials

Find an expression to represent the area of the shaded region