Evaluate
12\left(a-1\right)\left(2a+1\right)
Expand
24a^{2}-12a-12
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25a^{2}-20a+4-\left(a-4\right)^{2}
Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(5a-2\right)^{2}.
25a^{2}-20a+4-\left(a^{2}-8a+16\right)
Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-4\right)^{2}.
25a^{2}-20a+4-a^{2}+8a-16
To find the opposite of a^{2}-8a+16, find the opposite of each term.
24a^{2}-20a+4+8a-16
Combine 25a^{2} and -a^{2} to get 24a^{2}.
24a^{2}-12a+4-16
Combine -20a and 8a to get -12a.
24a^{2}-12a-12
Subtract 16 from 4 to get -12.
25a^{2}-20a+4-\left(a-4\right)^{2}
Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(5a-2\right)^{2}.
25a^{2}-20a+4-\left(a^{2}-8a+16\right)
Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-4\right)^{2}.
25a^{2}-20a+4-a^{2}+8a-16
To find the opposite of a^{2}-8a+16, find the opposite of each term.
24a^{2}-20a+4+8a-16
Combine 25a^{2} and -a^{2} to get 24a^{2}.
24a^{2}-12a+4-16
Combine -20a and 8a to get -12a.
24a^{2}-12a-12
Subtract 16 from 4 to get -12.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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y = 3x + 4
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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}