Question

please help 4th question

Answer 1

(4)

Given Equation is 125(2x + 3y)^3 - (2x - 3y)^3.

⇒ [5(2x + 3y)]^3 - (2x - 3y)^3

We know that a^3 - b^3 = (a - b)(a^2 + ab + b^2)

⇒ 5(2x + 3y) - (2x - 3y)[(5(2x + 3y)^2) + 5(2x + 3y)(2x - 3y) + (2x - 3y)^2]

⇒ 5(2x + 3y) - (2x - 3y)[(25(4x^2 + 9y^2 + 12xy + 5(4x^2 - 9y^2) + (4x^2 + 9y^2 - 12xy)]

⇒ (10x + 15y - 2x + 3y)[(100x^2 + 225y^2 + 300xy + 20x^2 - 45y^2 + 4x^2 + 9y^2 - 12xy)]

⇒ (8x + 18y)[124x^2 + 189y^2 + 288xy).

Therefore, the factor is (8x + 8y)[124x^2 + 189y^2 + 288xy]  --- Option (A).

Hope it helps!