A. Each rectangle has been subdivided into four smaller rectangles Write two exp

Question

A. Each rectangle has been subdivided into four smaller rectangles Write two expressions for the area of the rectangle outlined in red, one in factored form and one in expanded form. 1. 2. 3. 4. B. A square has sides of length x centimeters One dimension is doubled and then increased by 2 centimeters. The other dimension is increased by 3 centimeters. 1. Make a sketch of the new rectangle. Label the area of each section. 2. Write two expressions, one in factored form and one in expanded form, for the area of the new rectangle. c. Use a rectangle model to help write each expression in expanded form D. Carminda says she doesn't need a rectangle model to multiply (x 3) by (r + 2). She uses the Distributive Property (x+3)(x+ 2) (x+3)x+ (x+ 3)2 #x2 + 3x + 2x + 6 x2 + 5x + 6 1. Is Carminda correct? Explain what she did at each step 2. Show how using the Distributive Property to multiply (x +3) and (x + 5) is the same as using a rectangle model.

Explanation / Answer

1. A= (2+x)(5+x)

A= 10+2x+5x+ x 2=x 2+7x+10

2.A= (3+x)(x+3)

A=9+3x+3x+x 2=x 2+6x+9

3. A = (2+x)(4+x)

A=8+2x+4x+x 2=x 2+6x+8

4. A=(1+x)(x+x)=2x(1+x)

A= 2x +2x 2

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