Question

Factor completely. Drag the expressions into the box if they are part of the factored form of the polynomial. If the polynomial is not factorable, drag prime.

𝑔⁡𝑥^2 −3⁢ℎ⁡𝑥^2 −6⁢𝑓⁡𝑦^2 −𝑔⁡𝑦^2 +6⁢𝑓⁡𝑥^2 +3⁢ℎ⁡𝑦^2

Answer 1

Combine like terms: (g − 3h + 6f)x^2 + (−g + 3h − 6f)y^2 = (g − 3h + 6f)(x^2 − y^2)
Then x^2 − y^2 = (x − y)(x + y).

So the fully factored form is (g − 3h + 6f)(x − y)(x + y).