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81x^{2}-\left(81x^{2}+126xy+49y^{2}\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(9x+7y\right)^{2}.
81x^{2}-81x^{2}-126xy-49y^{2}
To find the opposite of 81x^{2}+126xy+49y^{2}, find the opposite of each term.
-126xy-49y^{2}
Combine 81x^{2} and -81x^{2} to get 0.
81x^{2}-\left(81x^{2}+126xy+49y^{2}\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(9x+7y\right)^{2}.
81x^{2}-81x^{2}-126xy-49y^{2}
To find the opposite of 81x^{2}+126xy+49y^{2}, find the opposite of each term.
-126xy-49y^{2}
Combine 81x^{2} and -81x^{2} to get 0.