Evaluate
15-12x-5x^{2}
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15-12x-5x^{2}
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x^{2}-6x+9-6\left(x^{2}+x-1\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.
x^{2}-6x+9-6x^{2}-6x+6
Use the distributive property to multiply -6 by x^{2}+x-1.
-5x^{2}-6x+9-6x+6
Combine x^{2} and -6x^{2} to get -5x^{2}.
-5x^{2}-12x+9+6
Combine -6x and -6x to get -12x.
-5x^{2}-12x+15
Add 9 and 6 to get 15.
x^{2}-6x+9-6\left(x^{2}+x-1\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.
x^{2}-6x+9-6x^{2}-6x+6
Use the distributive property to multiply -6 by x^{2}+x-1.
-5x^{2}-6x+9-6x+6
Combine x^{2} and -6x^{2} to get -5x^{2}.
-5x^{2}-12x+9+6
Combine -6x and -6x to get -12x.
-5x^{2}-12x+15
Add 9 and 6 to get 15.
Examples
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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
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