Question

Need help!! algebra!!!

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)

Answer 1

Explanation:

Part A

we have to solve the associated equation

4a^2 - 20a + 25 = 0

first of all we have to find the delta/4

Δ/4 = (b/2)^2 - ac where a is the term that multiply a^2, b is the term that multiply a and c is the therm without the variable

Δ/4 = (-10)^2 -100 = 100-100 = 0

the delta is equal to 0 that is mean that the equation has two coincident solutions, that can be find thanks to this formula

a1,a2 = -b/2/a = 10/4 = 5/2

now we can factorize the trinomial in this way:

4(a-5/2)(a-5/2)

4[(2a-5)/2][(2a-5)/2]

(2a-5)(2a-5)

the side of the square is 2a-5

Part B

the area of the rectangle is expressed as difference by two squares, so it can be rewritten as

(3a+4b)(3a-4b)

so the dimension of the rectangle are

3a+4b and 3a-4b

Answer 2

Explanation: