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