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

(𝑥 +𝑦)

prime

(𝑥 −𝑦)

6⁢𝑓 −𝑔 +3⁢ℎ

6⁢𝑓 +𝑔 −3⁢ℎ

𝑔⁡𝑥 −𝑔⁡𝑦 −3⁢ℎ⁡𝑥 +3⁢ℎ⁡𝑦 +6⁢𝑓⁡𝑥 −6⁢𝑓⁡𝑦

Answer 1

First combine like terms:
(6f + g − 3h)x^2 + (−6f − g + 3h)y^2
= (6f + g − 3h)(x^2 − y^2)
= (6f + g − 3h)(x − y)(x + y)

So drag in: (x + y), (x − y), 6f + g − 3h.