What is factor (m-n)^2-(2m+3n)^2 ?

The solution to factor (m-n)^2-(2m+3n)^2 is -(3m+2n)(m+4n)

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factor (m-n)^2-(2m+3n)^2

factor

(m - n)^{2} - (2 m + 3 n)^{2}

- (3 m + 2 n) (m + 4 n)

Solution steps

(m - n)^{2} - (2 m + 3 n)^{2}

Apply Difference of Two Squares Formula:

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

(m - n)^{2} - (2 m + 3 n)^{2} = ((m - n) + (2 m + 3 n)) ((m - n) - (2 m + 3 n))

= ((m - n) + (2 m + 3 n)) ((m - n) - (2 m + 3 n))

Simplify

((m - n) + (2 m + 3 n)) ((m - n) - (2 m + 3 n)) : (3 m + 2 n) (- m - 4 n)

= (3 m + 2 n) (- m - 4 n)

Factor

- m - 4 n : - (m + 4 n)

= (3 m + 2 n) (- (m + 4 n))

Apply rule:

a (- b) = - ab

(3 m + 2 n) (- (m + 4 n)) = - (3 m + 2 n) (m + 4 n)

= - (3 m + 2 n) (m + 4 n)

- \frac{2}{3} (- 3)

15 (1.2)^{10}

- 2 x \geq - 2

6 (n - 1) = 2 (2 n + 4)

25 a^{2} - 30 a + 9

What is factor (m-n)^2-(2m+3n)^2 ?
The solution to factor (m-n)^2-(2m+3n)^2 is -(3m+2n)(m+4n)