Evaluate
5y\left(x-2y\right)
Expand
5xy-10y^{2}
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x^{2}+xy-6y^{2}-\left(x-2y\right)^{2}
Use the distributive property to multiply x-2y by x+3y and combine like terms.
x^{2}+xy-6y^{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}.
x^{2}+xy-6y^{2}-x^{2}+4xy-4y^{2}
To find the opposite of x^{2}-4xy+4y^{2}, find the opposite of each term.
xy-6y^{2}+4xy-4y^{2}
Combine x^{2} and -x^{2} to get 0.
5xy-6y^{2}-4y^{2}
Combine xy and 4xy to get 5xy.
5xy-10y^{2}
Combine -6y^{2} and -4y^{2} to get -10y^{2}.
x^{2}+xy-6y^{2}-\left(x-2y\right)^{2}
Use the distributive property to multiply x-2y by x+3y and combine like terms.
x^{2}+xy-6y^{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}.
x^{2}+xy-6y^{2}-x^{2}+4xy-4y^{2}
To find the opposite of x^{2}-4xy+4y^{2}, find the opposite of each term.
xy-6y^{2}+4xy-4y^{2}
Combine x^{2} and -x^{2} to get 0.
5xy-6y^{2}-4y^{2}
Combine xy and 4xy to get 5xy.
5xy-10y^{2}
Combine -6y^{2} and -4y^{2} to get -10y^{2}.
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\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
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Limits
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