What is factor (p-2q)^2-(2p+q)^2 ?

The solution to factor (p-2q)^2-(2p+q)^2 is -(3p-q)(p+3q)

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factor (p-2q)^2-(2p+q)^2

factor

(p - 2 q)^{2} - (2 p + q)^{2}

- (3 p - q) (p + 3 q)

Solution steps

(p - 2 q)^{2} - (2 p + q)^{2}

Apply Difference of Two Squares Formula:

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

(p - 2 q)^{2} - (2 p + q)^{2} = ((p - 2 q) + (2 p + q)) ((p - 2 q) - (2 p + q))

= ((p - 2 q) + (2 p + q)) ((p - 2 q) - (2 p + q))

Simplify

((p - 2 q) + (2 p + q)) ((p - 2 q) - (2 p + q)) : (3 p - q) (- p - 3 q)

= (3 p - q) (- p - 3 q)

Factor

- p - 3 q : - (p + 3 q)

= (3 p - q) (- (p + 3 q))

Apply rule:

a (- b) = - ab

(3 p - q) (- (p + 3 q)) = - (3 p - q) (p + 3 q)

= - (3 p - q) (p + 3 q)

\frac{x + 1}{6} - \frac{x + 3}{4} = - 1

\frac{x}{2} - 5 = 7

x^{2} - 10 x = - 16

\frac{2}{3} x - \frac{6}{5} = \frac{1}{2} + \frac{5}{6} x

36 + x^{2} = 85

What is factor (p-2q)^2-(2p+q)^2 ?
The solution to factor (p-2q)^2-(2p+q)^2 is -(3p-q)(p+3q)