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-2x-4
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-2x-4
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-\frac{1}{4}xx-\frac{1}{4}x\times 8+\left(\frac{1}{2}x-2\right)\left(\frac{1}{2}x+2\right)
Use the distributive property to multiply -\frac{1}{4}x by x+8.
-\frac{1}{4}x^{2}-\frac{1}{4}x\times 8+\left(\frac{1}{2}x-2\right)\left(\frac{1}{2}x+2\right)
Multiply x and x to get x^{2}.
-\frac{1}{4}x^{2}+\frac{-8}{4}x+\left(\frac{1}{2}x-2\right)\left(\frac{1}{2}x+2\right)
Express -\frac{1}{4}\times 8 as a single fraction.
-\frac{1}{4}x^{2}-2x+\left(\frac{1}{2}x-2\right)\left(\frac{1}{2}x+2\right)
Divide -8 by 4 to get -2.
-\frac{1}{4}x^{2}-2x+\left(\frac{1}{2}x\right)^{2}-2^{2}
Consider \left(\frac{1}{2}x-2\right)\left(\frac{1}{2}x+2\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
-\frac{1}{4}x^{2}-2x+\left(\frac{1}{2}\right)^{2}x^{2}-2^{2}
Expand \left(\frac{1}{2}x\right)^{2}.
-\frac{1}{4}x^{2}-2x+\frac{1}{4}x^{2}-2^{2}
Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.
-\frac{1}{4}x^{2}-2x+\frac{1}{4}x^{2}-4
Calculate 2 to the power of 2 and get 4.
-2x-4
Combine -\frac{1}{4}x^{2} and \frac{1}{4}x^{2} to get 0.
-\frac{1}{4}xx-\frac{1}{4}x\times 8+\left(\frac{1}{2}x-2\right)\left(\frac{1}{2}x+2\right)
Use the distributive property to multiply -\frac{1}{4}x by x+8.
-\frac{1}{4}x^{2}-\frac{1}{4}x\times 8+\left(\frac{1}{2}x-2\right)\left(\frac{1}{2}x+2\right)
Multiply x and x to get x^{2}.
-\frac{1}{4}x^{2}+\frac{-8}{4}x+\left(\frac{1}{2}x-2\right)\left(\frac{1}{2}x+2\right)
Express -\frac{1}{4}\times 8 as a single fraction.
-\frac{1}{4}x^{2}-2x+\left(\frac{1}{2}x-2\right)\left(\frac{1}{2}x+2\right)
Divide -8 by 4 to get -2.
-\frac{1}{4}x^{2}-2x+\left(\frac{1}{2}x\right)^{2}-2^{2}
Consider \left(\frac{1}{2}x-2\right)\left(\frac{1}{2}x+2\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
-\frac{1}{4}x^{2}-2x+\left(\frac{1}{2}\right)^{2}x^{2}-2^{2}
Expand \left(\frac{1}{2}x\right)^{2}.
-\frac{1}{4}x^{2}-2x+\frac{1}{4}x^{2}-2^{2}
Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.
-\frac{1}{4}x^{2}-2x+\frac{1}{4}x^{2}-4
Calculate 2 to the power of 2 and get 4.
-2x-4
Combine -\frac{1}{4}x^{2} and \frac{1}{4}x^{2} to get 0.
Examples
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{ 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}