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

The solution to factor (m+2)^2-(m+2)+mn*(n+2)+2n(n+2) is (2+m)(n^2+2n+m+1)

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factor (m+2)^2-(m+2)+mn*(n+2)+2n(n+2)

factor

(m + 2)^{2} - (m + 2) + mn \cdot (n + 2) + 2 n (n + 2)

(2 + m) (n^{2} + 2 n + m + 1)

Solution steps

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

Apply exponent rule:

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

(2 + m)^{2} = (2 + m) (2 + m)

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

Rewrite as

= (2 + m) (2 + m) - 1 \cdot (2 + m) + mn (2 + n) + 2 n (2 + n)

Factor out common term

(2 + m)

= (2 + m) (2 + m - 1) + mn (2 + n) + 2 n (2 + n)

Factor out common term

n (2 + n)

= (2 + m) (- 1 + 2 + m) + n (2 + n) (m + 2)

Rewrite as

= (2 + m) (- 1 + 2 + m) + (2 + m) n (2 + n)

Factor out common term

(2 + m)

= (2 + m) (- 1 + 2 + m + n (2 + n))

Expand

m + n (n + 2) + 2 - 1 : n^{2} + 2 n + m + 1

= (m + 2) (n^{2} + 2 n + m + 1)

5 x^{2} + 3 x - 8

\frac{1}{X + 4} \leq 7

\frac{p}{3} - \frac{3}{2} = - \frac{5}{4}

25 x^{2} - 36 y^{8}

5 = x + 2

What is factor (m+2)^2-(m+2)+mn*(n+2)+2n(n+2) ?
The solution to factor (m+2)^2-(m+2)+mn*(n+2)+2n(n+2) is (2+m)(n^2+2n+m+1)