What is factor (2a-b)(2x-2y)^2-(6a-3b)^3(x-y) ?

The solution to factor (2a-b)(2x-2y)^2-(6a-3b)^3(x-y) is (-b+2a)(x-y)(4(x-y)-27(-b+2a)^2)

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factor (2a-b)(2x-2y)^2-(6a-3b)^3(x-y)

factor

(2 a - b) (2 x - 2 y)^{2} - (6 a - 3 b)^{3} (x - y)

(- b + 2 a) (x - y) (4 (x - y) - 27 (- b + 2 a)^{2})

Solution steps

(2 a - b) (2 x - 2 y)^{2} - (6 a - 3 b)^{3} (x - y)

(2 a - b) (2 x - 2 y)^{2} = 4 (2 a - b) (x - y)^{2}

(6 a - 3 b)^{3} (x - y) = 3^{3} (2 a - b)^{3} (x - y)

= 4 (2 a - b) (x - y)^{2} - 3^{3} (2 a - b)^{3} (x - y)

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

(x - y)^{2} = (x - y) (x - y), (- b + 2 a)^{3} = (- b + 2 a) (- b + 2 a)^{2}

= 4 (- b + 2 a) (x - y) (x - y) - 27 (- b + 2 a) (- b + 2 a)^{2} (x - y)

Factor out common term

(- b + 2 a) (x - y)

= (- b + 2 a) (x - y) (4 (x - y) - 27 (- b + 2 a)^{2})

(y^{\frac{1}{2}})^{2}

w^{2} + 6 w + 9 = 0

8 x^{2} - 50 y^{2}

∣ 2 x + 9 ∣ > 17

z^{2} - 12 z + 20

What is factor (2a-b)(2x-2y)^2-(6a-3b)^3(x-y) ?
The solution to factor (2a-b)(2x-2y)^2-(6a-3b)^3(x-y) is (-b+2a)(x-y)(4(x-y)-27(-b+2a)^2)