Evaluate
-4y\left(x+2y\right)
Expand
-4xy-8y^{2}
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-4y^{2}+x^{2}-\left(x+2y\right)^{2}
Use the distributive property to multiply -2y-x by 2y-x and combine like terms.
-4y^{2}+x^{2}-\left(x^{2}+4xy+4y^{2}\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+2y\right)^{2}.
-4y^{2}+x^{2}-x^{2}-4xy-4y^{2}
To find the opposite of x^{2}+4xy+4y^{2}, find the opposite of each term.
-4y^{2}-4xy-4y^{2}
Combine x^{2} and -x^{2} to get 0.
-8y^{2}-4xy
Combine -4y^{2} and -4y^{2} to get -8y^{2}.
-4y^{2}+x^{2}-\left(x+2y\right)^{2}
Use the distributive property to multiply -2y-x by 2y-x and combine like terms.
-4y^{2}+x^{2}-\left(x^{2}+4xy+4y^{2}\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+2y\right)^{2}.
-4y^{2}+x^{2}-x^{2}-4xy-4y^{2}
To find the opposite of x^{2}+4xy+4y^{2}, find the opposite of each term.
-4y^{2}-4xy-4y^{2}
Combine x^{2} and -x^{2} to get 0.
-8y^{2}-4xy
Combine -4y^{2} and -4y^{2} to get -8y^{2}.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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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
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Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}