What is factor m^2n+2m^2+mn+2m+n+2 ?

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

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factor m^2n+2m^2+mn+2m+n+2

factor

m^{2} n + 2 m^{2} + mn + 2 m + n + 2

(1 + m (1 + m)) (n + 2)

Solution steps

m^{2} n + 2 m^{2} + mn + 2 m + n + 2

Apply exponent rule:

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

m^{2} = mm

= mmn + 2 mm + mn + 2 m + n + 2

Factor out common term

nm

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

Factor out common term

n

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

Apply exponent rule:

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

m^{2} = mm

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

Rewrite as

= n (1 + (1 + m) m) + 2 mm + 1 \cdot 2 m + 2

Factor out common term

2 m

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

Rewrite as

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

Factor out common term

2

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

Factor out common term

(1 + (1 + m) m)

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

(9 z^{3}) - 2 y

R (v) d v

(a^{2} - 1)^{3} - 27

γ (0.5)

- 2 + lo g_{a + b} (a^{2} - b^{2})

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