Factoring Polynomials| Algebra| ENGG10 LE1 Problem 10

Factor the polynomials completely.

81y^4-256

SOLUTION:

We know that 81y^4=\left(9y^2\right)^2 and 256=\left(16\right)^2. Therefore, we are given a difference of two squares.

The factors are

=\left(9y^2-16\right)\left(9y^2+16\right)

The factor \left(9y^2-16\right) is also difference of two squares. So, we can further factor out the factors as

=\left(3y+4\right)\left(3y-4\right)\left(9y^2+16\right)