Question

Which expression is equivalent to 36x2 − 100? a. 4(3x − 5)(3x − 5)

b. 4(3x + 5)(3x − 5)
c. 2(9x − 25)(9x − 25) d. 2(9x + 25)(9x − 25)

Answer 1

b. 4(3x + 5)(3x - 5)

Explanation:

Recall difference of squares general formula as a² - b² = (a+b)(a-b)

Looking at the question we have 36x² - 100

Looking at the given answer choices we see there is some factor multiplied through the difference of squares, so we pull out the greatest common factor from the question to get 36x² - 100 = 4(9x² - 25). Now apply difference of squares where a² = 9x² and b² = 25 to get a = 3x and b = 5. Now the equation becomes b. 4(3x + 5)(3x - 5)