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.

12⁢𝑎⁢𝑥^2 −20⁢𝑐⁢𝑦^2 −18⁢𝑏⁢𝑥^2 −10⁢𝑎⁢𝑦^2 +15⁢𝑏⁢𝑦^2 +24⁢𝑐⁢𝑥^2

prime

(6⁢𝑥^2 −5⁢𝑦^2)

(2⁢𝑎 −3⁢𝑏 +4⁢𝑐)

12⁢𝑎⁢𝑥^2 −10⁢𝑎⁢𝑦^2

18⁢𝑏⁢𝑥^2 −15⁢𝑏⁢𝑦

24⁢𝑐⁢𝑥^2 −20⁢𝑐⁢𝑦^2

Answer 1

Factor completely:

Group x^2 and y^2 terms:

x^2(12a −18b +24c) + y^2(−10a +15b −20c)
= x^2·6(2a −3b +4c) + y^2·(−5)(2a −3b +4c)
= (2a −3b +4c)(6x^2 −5y^2).

So drag (2a −3b +4c) and (6x^2 −5y^2).