Evaluate
4\left(b^{2}-4\right)
Expand
4b^{2}-16
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5b^{2}+8b-\left(b+4\right)^{2}
Use the distributive property to multiply b by 5b+8.
5b^{2}+8b-\left(b^{2}+8b+16\right)
Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(b+4\right)^{2}.
5b^{2}+8b-b^{2}-8b-16
To find the opposite of b^{2}+8b+16, find the opposite of each term.
4b^{2}+8b-8b-16
Combine 5b^{2} and -b^{2} to get 4b^{2}.
4b^{2}-16
Combine 8b and -8b to get 0.
5b^{2}+8b-\left(b+4\right)^{2}
Use the distributive property to multiply b by 5b+8.
5b^{2}+8b-\left(b^{2}+8b+16\right)
Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(b+4\right)^{2}.
5b^{2}+8b-b^{2}-8b-16
To find the opposite of b^{2}+8b+16, find the opposite of each term.
4b^{2}+8b-8b-16
Combine 5b^{2} and -b^{2} to get 4b^{2}.
4b^{2}-16
Combine 8b and -8b to get 0.
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}