Evaluate
3x^{2}+13xy+2y^{2}
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3x^{2}+13xy+2y^{2}
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2\left(4x^{2}+4xy+y^{2}\right)-5x\left(x-y\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+y\right)^{2}.
8x^{2}+8xy+2y^{2}-5x\left(x-y\right)
Use the distributive property to multiply 2 by 4x^{2}+4xy+y^{2}.
8x^{2}+8xy+2y^{2}-5x^{2}+5xy
Use the distributive property to multiply -5x by x-y.
3x^{2}+8xy+2y^{2}+5xy
Combine 8x^{2} and -5x^{2} to get 3x^{2}.
3x^{2}+13xy+2y^{2}
Combine 8xy and 5xy to get 13xy.
2\left(4x^{2}+4xy+y^{2}\right)-5x\left(x-y\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+y\right)^{2}.
8x^{2}+8xy+2y^{2}-5x\left(x-y\right)
Use the distributive property to multiply 2 by 4x^{2}+4xy+y^{2}.
8x^{2}+8xy+2y^{2}-5x^{2}+5xy
Use the distributive property to multiply -5x by x-y.
3x^{2}+8xy+2y^{2}+5xy
Combine 8x^{2} and -5x^{2} to get 3x^{2}.
3x^{2}+13xy+2y^{2}
Combine 8xy and 5xy to get 13xy.
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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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