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

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

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

simplify

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

m^{2} + 3 m + m n^{2} + 2 mn + 2 n^{2} + 4 n + 2

Solution steps

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

Apply the distributive law:

- (a + b) = - a - b

- (m + 2) = - m - 2

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

Expand

(m + 2)^{2} : m^{2} + 4 m + 4

= m^{2} + 4 m + 4 - m - 2 + mn (n + 2) + 2 n (n + 2)

Expand

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

= m^{2} + 4 m + 4 - m - 2 + m n^{2} + 2 mn + 2 n (n + 2)

Expand

2 n (n + 2) : 2 n^{2} + 4 n

= m^{2} + 4 m + 4 - m - 2 + m n^{2} + 2 mn + 2 n^{2} + 4 n

Group like terms

= m^{2} + 4 m - m + m n^{2} + 2 mn + 2 n^{2} + 4 n + 4 - 2

Add similar elements:

4 m - m = 3 m

= m^{2} + 3 m + m n^{2} + 2 mn + 2 n^{2} + 4 n + 4 - 2

Subtract the numbers:

4 - 2 = 2

= m^{2} + 3 m + m n^{2} + 2 mn + 2 n^{2} + 4 n + 2

5^{2} + 5^{2}

m^{3} - 12 m + 16

x^{2} + 48 = 0

6 x^{2} + 5 x - 4 = 0

\frac{d}{d t} (\frac{m - t}{n})

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