Evaluate
y\left(4x+5y\right)
Expand
4xy+5y^{2}
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x^{2}+4xy+4y^{2}-\left(x+y\right)\left(x-y\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+2y\right)^{2}.
x^{2}+4xy+4y^{2}-\left(x^{2}-y^{2}\right)
Consider \left(x+y\right)\left(x-y\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
x^{2}+4xy+4y^{2}-x^{2}+y^{2}
To find the opposite of x^{2}-y^{2}, find the opposite of each term.
4xy+4y^{2}+y^{2}
Combine x^{2} and -x^{2} to get 0.
4xy+5y^{2}
Combine 4y^{2} and y^{2} to get 5y^{2}.
x^{2}+4xy+4y^{2}-\left(x+y\right)\left(x-y\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+2y\right)^{2}.
x^{2}+4xy+4y^{2}-\left(x^{2}-y^{2}\right)
Consider \left(x+y\right)\left(x-y\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
x^{2}+4xy+4y^{2}-x^{2}+y^{2}
To find the opposite of x^{2}-y^{2}, find the opposite of each term.
4xy+4y^{2}+y^{2}
Combine x^{2} and -x^{2} to get 0.
4xy+5y^{2}
Combine 4y^{2} and y^{2} to get 5y^{2}.
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}