PLS HELP ASAP BRAINLIEST 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)

The length of each side of the square is "2x - 5" units.

The dimensions of the rectangle are "3a - 4b" by "3a + 4b".

Step-by-step explanation:

Part A:

Factoring a quadratic equation gives two linear equations. Considering all sides of a square are equal, the two linear factors of the quadratic function must also be equal. Thus, taking the square root of 4 and 25 will give us the coefficient and constant "a" and "b" respectively in the factor (ax + b).

(4a^2 - 20a + 25) = (ax + b) * (ax + b)

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

However, the quadratic equation specifies "-20a". Make sure you are accounting for this by making the 5's negative.

Correct (2x - 5) * (2x - 5)

The length of each side of the square is "2x - 5" units.

Part b:

This quadratic equation has no variable "ab", which means that the correct answer must fall into the form (ax - by) * (ax + by).

You can use the "difference of squares" formula to find the answer above.

The difference of squares states that:

The square root of 9a^2 is 3a and the square root of 16b^2 is 4b, so substituting these values into the equation, we get:

The dimensions of the rectangle are "3a - 4b" by "3a + 4b".

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