Evaluate
5\left(a^{2}+1\right)
Expand
5a^{2}+5
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4a^{2}+4a+1+\left(a-2\right)^{2}
Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(2a+1\right)^{2}.
4a^{2}+4a+1+a^{2}-4a+4
Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-2\right)^{2}.
5a^{2}+4a+1-4a+4
Combine 4a^{2} and a^{2} to get 5a^{2}.
5a^{2}+1+4
Combine 4a and -4a to get 0.
5a^{2}+5
Add 1 and 4 to get 5.
4a^{2}+4a+1+\left(a-2\right)^{2}
Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(2a+1\right)^{2}.
4a^{2}+4a+1+a^{2}-4a+4
Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-2\right)^{2}.
5a^{2}+4a+1-4a+4
Combine 4a^{2} and a^{2} to get 5a^{2}.
5a^{2}+1+4
Combine 4a and -4a to get 0.
5a^{2}+5
Add 1 and 4 to get 5.
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}