Evaluate
4\left(2m+n+3\right)\left(3m+2n+1\right)
Expand
24m^{2}+28mn+44m+8n^{2}+28n+12
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24m^{2}+16mn+8m+12nm+8n^{2}+4n+36m+24n+12
Apply the distributive property by multiplying each term of 4m+2n+6 by each term of 6m+4n+2.
24m^{2}+28mn+8m+8n^{2}+4n+36m+24n+12
Combine 16mn and 12nm to get 28mn.
24m^{2}+28mn+44m+8n^{2}+4n+24n+12
Combine 8m and 36m to get 44m.
24m^{2}+28mn+44m+8n^{2}+28n+12
Combine 4n and 24n to get 28n.
24m^{2}+16mn+8m+12nm+8n^{2}+4n+36m+24n+12
Apply the distributive property by multiplying each term of 4m+2n+6 by each term of 6m+4n+2.
24m^{2}+28mn+8m+8n^{2}+4n+36m+24n+12
Combine 16mn and 12nm to get 28mn.
24m^{2}+28mn+44m+8n^{2}+4n+24n+12
Combine 8m and 36m to get 44m.
24m^{2}+28mn+44m+8n^{2}+28n+12
Combine 4n and 24n to get 28n.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}