Evaluate
8x^{2}-3
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8x^{2}-3
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4\left(\left(\frac{3}{2}x\right)^{2}-\frac{x^{2}+3}{4}\right)
Combine x and \frac{x}{2} to get \frac{3}{2}x.
4\left(\left(\frac{3}{2}\right)^{2}x^{2}-\frac{x^{2}+3}{4}\right)
Expand \left(\frac{3}{2}x\right)^{2}.
4\left(\frac{9}{4}x^{2}-\frac{x^{2}+3}{4}\right)
Calculate \frac{3}{2} to the power of 2 and get \frac{9}{4}.
9x^{2}+4\left(-\frac{x^{2}+3}{4}\right)
Use the distributive property to multiply 4 by \frac{9}{4}x^{2}-\frac{x^{2}+3}{4}.
9x^{2}-\left(x^{2}+3\right)
Cancel out 4 and 4.
9x^{2}-x^{2}-3
To find the opposite of x^{2}+3, find the opposite of each term.
8x^{2}-3
Combine 9x^{2} and -x^{2} to get 8x^{2}.
4\left(\left(\frac{3}{2}x\right)^{2}-\frac{x^{2}+3}{4}\right)
Combine x and \frac{x}{2} to get \frac{3}{2}x.
4\left(\left(\frac{3}{2}\right)^{2}x^{2}-\frac{x^{2}+3}{4}\right)
Expand \left(\frac{3}{2}x\right)^{2}.
4\left(\frac{9}{4}x^{2}-\frac{x^{2}+3}{4}\right)
Calculate \frac{3}{2} to the power of 2 and get \frac{9}{4}.
9x^{2}+4\left(-\frac{x^{2}+3}{4}\right)
Use the distributive property to multiply 4 by \frac{9}{4}x^{2}-\frac{x^{2}+3}{4}.
9x^{2}-\left(x^{2}+3\right)
Cancel out 4 and 4.
9x^{2}-x^{2}-3
To find the opposite of x^{2}+3, find the opposite of each term.
8x^{2}-3
Combine 9x^{2} and -x^{2} to get 8x^{2}.
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y = 3x + 4
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\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}