Question

PLEASE I NEED A REAL ANWSER NO LIES

Part A: The area of a square is (9a2 − 24a + 16) 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 (25a2 − 36b2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work. (5 points)

Answer 1

(3a - 4 )^2

Explanation:

(9a^2-24a+16)=(3a - 4 )^2

Therefore the length of each side of the square is (3a - 4 )^2

Answer 2

Part A: (3a - 4)^2

Part B: (5a + 6b)(5a - 6b)

Explanation:

Part A:

It looks like this is the square of a binomial. Now we check it.

9a^2 is the square of 3a.

16 is the square of 4 and of -4.

Check the middle term:

2 * 3a * 4 = 24a

2 * 3a * (-4) = -24a

Since we get -24a when we use 4, the second term of the binomial is 4.

Answer:

9a^2 - 24a + 16 = (3a - 4)^2

Part B:

25a^2 − 36b^2

This is a two-term polynomial. The two terms are perfect squares and there is a subtraction sign between them, so this is the difference of two squares. The difference of two squares factors into the product of a sum and a difference.

25a^2 is the square of 5a.

36b^2 is the square of 6b.

25a^2 − 36b^2 = (5a + 6b)(5a - 6b)