Algebra 2 Math question

Question

I have a test tomorrow and i am studying but i am stuck on this problem any help would be greatly appreciated. The problem is to factor 54x^3y - 16y^4.

Answer 1

Always start with GCF factoring. The GCF of 54x³y - 16y⁴ is 2y so we have:

54x³y - 16y⁴

2y(27x³ - 8y³) which is a difference of cubes where a = 3x and b is 2y

2y(3x - 2y)(9x² + 6xy + 4y⁴)

Hope this helps!

Answer 2

Recall: A³ - B³ = (A - B)(A² + AB + B²)

54x³y - 16y⁴ = 2y(27x³ - 8y³) = 2y[(3x)³ - (2y)³] = 2y(3x - 2y)[(3x)² + (3x)(2y) + (2y)²] =

2y(3x - 2y)(9x² + 6xy + 4y²)