Evaluate
8\left(1-2x\right)^{2}x^{4}
Expand
32x^{6}-32x^{5}+8x^{4}
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2x^{2}\left(4x^{2}-16xx^{2}+16\left(x^{2}\right)^{2}\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-4x^{2}\right)^{2}.
2x^{2}\left(4x^{2}-16x^{3}+16\left(x^{2}\right)^{2}\right)
To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.
2x^{2}\left(4x^{2}-16x^{3}+16x^{4}\right)
To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.
8x^{4}-32x^{5}+32x^{6}
Use the distributive property to multiply 2x^{2} by 4x^{2}-16x^{3}+16x^{4}.
2x^{2}\left(4x^{2}-16xx^{2}+16\left(x^{2}\right)^{2}\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-4x^{2}\right)^{2}.
2x^{2}\left(4x^{2}-16x^{3}+16\left(x^{2}\right)^{2}\right)
To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.
2x^{2}\left(4x^{2}-16x^{3}+16x^{4}\right)
To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.
8x^{4}-32x^{5}+32x^{6}
Use the distributive property to multiply 2x^{2} by 4x^{2}-16x^{3}+16x^{4}.
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}