Factor completely.

Question

16x^2 - 24xy + 9y^2

Select the correct choice below.

(a) 16x^2 - 24xy+ 9y^2=?

(b) The polynomial is prime.

Answer 1

This polynomial is not prime since it has the factors.

1) Fastest and easiest way to solve this problem is to remember the formula for (a+b)² and observe the pattern.

We know that, a²+2ab+b² =(a+b)²

16x² - 24xy + 9y² = (4x)² - 2.4x.3y + (3y)²

=(4x-3y)²

2) If you do not remember the formula, you can do the factoring the usual way

a.b = 16 x 9 = 144 = 1 x 2 x 2 x 2 x 2 x 3 x 3 = -12 x -12

a+b = -24 = (-12) + (-12)

This gives us two factors of a=-12 and b=-12

16x² - 24xy + 9y²

= 16x² - 12xy -12xy +9y²

= 4x (4x-3y) -3y(4x-3y)

= (4x-3y)(4x-3y)

=(4x-3y)²