Question

A square deck has a side length of x + 5. You are expanding the deck so that each side is four times as long as the side length of the original deck. What is the area of the new deck? Write your answer in standard form.

a) Identify and write an expression for the new side length of the deck.

















b) Apply and write an expression for the area of the new deck.

















c) What is the standard form of the expression for the area of the new deck?

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Answer 1

The new Lenth is 4x + 20 or 4(x + 5)

The are of the new deck is 16(x² + 10x + 25)

Explanation:

The original length of a deck is x + 5

If we do a 4 times expansion on it, we will have the new length to be

4(x + 5) = 4x + 20

The Area of the new square deck = area of square = Length²

Area = (4x + 20)²

= (4x + 20)(4x + 20)

= 16x² + 80x + 80x + 400

= 16x² + 160x + 400

= 16(x² + 10x + 25)