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36x^{2}-124x+89
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36x^{2}-124x+89
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10\left(4x^{2}-12x+9\right)-\left(-2x-1\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(-2x+3\right)^{2}.
40x^{2}-120x+90-\left(-2x-1\right)^{2}
Use the distributive property to multiply 10 by 4x^{2}-12x+9.
40x^{2}-120x+90-\left(4x^{2}+4x+1\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(-2x-1\right)^{2}.
40x^{2}-120x+90-4x^{2}-4x-1
To find the opposite of 4x^{2}+4x+1, find the opposite of each term.
36x^{2}-120x+90-4x-1
Combine 40x^{2} and -4x^{2} to get 36x^{2}.
36x^{2}-124x+90-1
Combine -120x and -4x to get -124x.
36x^{2}-124x+89
Subtract 1 from 90 to get 89.
10\left(4x^{2}-12x+9\right)-\left(-2x-1\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(-2x+3\right)^{2}.
40x^{2}-120x+90-\left(-2x-1\right)^{2}
Use the distributive property to multiply 10 by 4x^{2}-12x+9.
40x^{2}-120x+90-\left(4x^{2}+4x+1\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(-2x-1\right)^{2}.
40x^{2}-120x+90-4x^{2}-4x-1
To find the opposite of 4x^{2}+4x+1, find the opposite of each term.
36x^{2}-120x+90-4x-1
Combine 40x^{2} and -4x^{2} to get 36x^{2}.
36x^{2}-124x+90-1
Combine -120x and -4x to get -124x.
36x^{2}-124x+89
Subtract 1 from 90 to get 89.
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y = 3x + 4
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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}