Question

Part A: The area of a square is (4x2 + 20x + 25) square units. Determine the length of each side of the square by factoring the area expression completely. Show your work. (5 points)

Part B: The area of a rectangle is (4x2 − 9y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work. (5 points)

Answer 1

Part A is (2x+5)^2. Part B is (2x+3y)(2x-3y).

Explanation:

Part A: The polynomial is prime. When you split the middle term, it becomes 4x^2+10x+10x+25. Then rewrite using the common factor from the two pairs. 2x(2x+5)+5(2x+5). Rewrite in factored form, which is (2x+5)(2x+5). Then combine which is, (2x+5)^2. The length of each side is (2x+5)^2.

Part B: The polynomial is prime. Rewrite 4x^2 as (2x)^2 and 9y^2 as (3y)^2, which looks like (2x)^2-(3y)^2. Both terms are perfect squares. The answer is (2x+3y)(2x-3y).

Answer 2

Explanation:

4x² + 20x + 25 = (2x)² + 2* 2x *5 + 5²

{Compare with a² + 2ab + b² = (a+ b)²}

= (2x + 5)²

= (2x +5)*(2x+5)

Side of the square = 2x+ 5