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BRAINLIEST AND HELLA POINTS Part A: The area of a square is (4a2 − 20a + 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 (9a2 − 16b2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work. (5 points)

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Answer:

Hey there!

4a^2-20a+25 can be factored to (2a-5)(2a-5). Thus, the side length of the square is 2a-5. Basically, we want to find two of the same binomials that can multiply to get 4a^2-20a+25. For example, 2a times 2a = 4a^2, and you can use the foil method to solve for the rest.

4a^2 - 20a +25

(2a)^2 - 20a + (-5)^2

(2a - 5)^2

(9a2 − 16b2) is just a difference of squares, and can be factored to (3a+4b) and (3a-4b). The difference of squares formula can give us this.

Let me know if this helps :)

CSMedrano

Answer:

Step-by-step explanation:

Part A

[tex]4a^{2} -20a+25\\\\=(2a)^2-2(5)(2a)+5^2[/tex]

does that seems familiar?

it's because it's a perfect square that can be factorized as

[tex](2a-5)^2[/tex]

so the length of each side is

2a-5 both of them

Part B

[tex]9a^2-16b^2[/tex]

[tex](3a)^2-(4b)^2[/tex]

that's a difference of squares you know [tex]x^2-y^2=(x-y)(x+y)[/tex]

so

[tex](3a-4b)(3a+4b)[/tex]

so the lengths are

3a-4b and 3a+4b