Evaluate
\left(1-3x\right)\left(9x+1\right)
Expand
1+6x-27x^{2}
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2-18x^{2}-\left(-3x+1\right)^{2}
Use the distributive property to multiply 1-3x by 2+6x and combine like terms.
2-18x^{2}-\left(9x^{2}-6x+1\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(-3x+1\right)^{2}.
2-18x^{2}-9x^{2}+6x-1
To find the opposite of 9x^{2}-6x+1, find the opposite of each term.
2-27x^{2}+6x-1
Combine -18x^{2} and -9x^{2} to get -27x^{2}.
1-27x^{2}+6x
Subtract 1 from 2 to get 1.
2-18x^{2}-\left(-3x+1\right)^{2}
Use the distributive property to multiply 1-3x by 2+6x and combine like terms.
2-18x^{2}-\left(9x^{2}-6x+1\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(-3x+1\right)^{2}.
2-18x^{2}-9x^{2}+6x-1
To find the opposite of 9x^{2}-6x+1, find the opposite of each term.
2-27x^{2}+6x-1
Combine -18x^{2} and -9x^{2} to get -27x^{2}.
1-27x^{2}+6x
Subtract 1 from 2 to get 1.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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y = 3x + 4
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Matrix
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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}