What is factor (ax-3b)^2-(bx-3a)^2 ?

The solution to factor (ax-3b)^2-(bx-3a)^2 is (ax-3a-3b+bx)(ax+3a-3b-bx)

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factor (ax-3b)^2-(bx-3a)^2

factor

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

(a x - 3 a - 3 b + b x) (a x + 3 a - 3 b - b x)

Solution steps

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

Apply Difference of Two Squares Formula:

x^{2} - y^{2} = (x + y) (x - y)

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

= ((a x - 3 b) + (b x - 3 a)) ((a x - 3 b) - (b x - 3 a))

Simplify

((a x - 3 b) + (b x - 3 a)) ((a x - 3 b) - (b x - 3 a)) : (a x - 3 b + b x - 3 a) (a x - 3 b - b x + 3 a)

= (a x - 3 b + b x - 3 a) (a x - 3 b - b x + 3 a)

= (a x - 3 a - 3 b + b x) (a x + 3 a - 3 b - b x)

\frac{- 4}{( - 2 )}

- \frac{16}{25} \div \frac{8}{5}

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

(3 t - 2) (7 t - 5)

- 2 x (8 x)

What is factor (ax-3b)^2-(bx-3a)^2 ?
The solution to factor (ax-3b)^2-(bx-3a)^2 is (ax-3a-3b+bx)(ax+3a-3b-bx)