Evaluate
\left(x-2\right)\left(10x-7\right)
Expand
10x^{2}-27x+14
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4x^{2}-28x+49-\left(2x+5\right)\left(-3x+7\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(-2x+7\right)^{2}.
4x^{2}-28x+49-\left(-6x^{2}-x+35\right)
Use the distributive property to multiply 2x+5 by -3x+7 and combine like terms.
4x^{2}-28x+49+6x^{2}+x-35
To find the opposite of -6x^{2}-x+35, find the opposite of each term.
10x^{2}-28x+49+x-35
Combine 4x^{2} and 6x^{2} to get 10x^{2}.
10x^{2}-27x+49-35
Combine -28x and x to get -27x.
10x^{2}-27x+14
Subtract 35 from 49 to get 14.
4x^{2}-28x+49-\left(2x+5\right)\left(-3x+7\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(-2x+7\right)^{2}.
4x^{2}-28x+49-\left(-6x^{2}-x+35\right)
Use the distributive property to multiply 2x+5 by -3x+7 and combine like terms.
4x^{2}-28x+49+6x^{2}+x-35
To find the opposite of -6x^{2}-x+35, find the opposite of each term.
10x^{2}-28x+49+x-35
Combine 4x^{2} and 6x^{2} to get 10x^{2}.
10x^{2}-27x+49-35
Combine -28x and x to get -27x.
10x^{2}-27x+14
Subtract 35 from 49 to get 14.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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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
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}