Evaluate
3\left(x-2y\right)\left(x+4y\right)
Expand
3x^{2}+6xy-24y^{2}
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4x^{2}-4xy+y^{2}-\left(x-5y\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-y\right)^{2}.
4x^{2}-4xy+y^{2}-\left(x^{2}-10xy+25y^{2}\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-5y\right)^{2}.
4x^{2}-4xy+y^{2}-x^{2}+10xy-25y^{2}
To find the opposite of x^{2}-10xy+25y^{2}, find the opposite of each term.
3x^{2}-4xy+y^{2}+10xy-25y^{2}
Combine 4x^{2} and -x^{2} to get 3x^{2}.
3x^{2}+6xy+y^{2}-25y^{2}
Combine -4xy and 10xy to get 6xy.
3x^{2}+6xy-24y^{2}
Combine y^{2} and -25y^{2} to get -24y^{2}.
4x^{2}-4xy+y^{2}-\left(x-5y\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-y\right)^{2}.
4x^{2}-4xy+y^{2}-\left(x^{2}-10xy+25y^{2}\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-5y\right)^{2}.
4x^{2}-4xy+y^{2}-x^{2}+10xy-25y^{2}
To find the opposite of x^{2}-10xy+25y^{2}, find the opposite of each term.
3x^{2}-4xy+y^{2}+10xy-25y^{2}
Combine 4x^{2} and -x^{2} to get 3x^{2}.
3x^{2}+6xy+y^{2}-25y^{2}
Combine -4xy and 10xy to get 6xy.
3x^{2}+6xy-24y^{2}
Combine y^{2} and -25y^{2} to get -24y^{2}.
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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 ) }
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\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
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