Evaluate
\left(5y-x\right)\left(5x+9y\right)
Expand
45y^{2}+16xy-5x^{2}
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4x^{2}+28xy+49y^{2}-\left(3x+2y\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+7y\right)^{2}.
4x^{2}+28xy+49y^{2}-\left(9x^{2}+12xy+4y^{2}\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3x+2y\right)^{2}.
4x^{2}+28xy+49y^{2}-9x^{2}-12xy-4y^{2}
To find the opposite of 9x^{2}+12xy+4y^{2}, find the opposite of each term.
-5x^{2}+28xy+49y^{2}-12xy-4y^{2}
Combine 4x^{2} and -9x^{2} to get -5x^{2}.
-5x^{2}+16xy+49y^{2}-4y^{2}
Combine 28xy and -12xy to get 16xy.
-5x^{2}+16xy+45y^{2}
Combine 49y^{2} and -4y^{2} to get 45y^{2}.
4x^{2}+28xy+49y^{2}-\left(3x+2y\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+7y\right)^{2}.
4x^{2}+28xy+49y^{2}-\left(9x^{2}+12xy+4y^{2}\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3x+2y\right)^{2}.
4x^{2}+28xy+49y^{2}-9x^{2}-12xy-4y^{2}
To find the opposite of 9x^{2}+12xy+4y^{2}, find the opposite of each term.
-5x^{2}+28xy+49y^{2}-12xy-4y^{2}
Combine 4x^{2} and -9x^{2} to get -5x^{2}.
-5x^{2}+16xy+49y^{2}-4y^{2}
Combine 28xy and -12xy to get 16xy.
-5x^{2}+16xy+45y^{2}
Combine 49y^{2} and -4y^{2} to get 45y^{2}.
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