Question

. Part 1: Diana factored 75a2 + 27d2 using the following steps.

75a2 + 27d2 = 3(25a2 + 9d2)
= 3(5a + 3d)(5a − 3d)

Determine whether Diana factored this binomial correctly. If not, use complete sentences to explain what she did wrong and how she could check her factors for accuracy in the future.

Part 2: Create a unique binomial that contains a GCF and a difference of two squares. Factor your binomial completely, showing all steps.

Answer 1

The Factoring is correct..

for part 2

Let x be a variable.
Let y be the other variable.

a(x^2 - y^2 )
= ax^2 - ay^2

Answer 2

The first step is fine, but 25a² + 9d² does not factor (it's prime). It would need to be the DIFFERENCE of two squares:
25a² - 9d² = (5a - 3d)(5a + 3d)

it's easy to create a unique binomial with a GCF and difference of two squares.

difference of squares: 4x² - 9y²
with GCF of 2: 8x² - 18y²