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\left(2x\right)^{2}-\left(7y\right)^{2}+\left(x-7y\right)^{2}
Consider \left(2x+7y\right)\left(2x-7y\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
2^{2}x^{2}-\left(7y\right)^{2}+\left(x-7y\right)^{2}
Expand \left(2x\right)^{2}.
4x^{2}-\left(7y\right)^{2}+\left(x-7y\right)^{2}
Calculate 2 to the power of 2 and get 4.
4x^{2}-7^{2}y^{2}+\left(x-7y\right)^{2}
Expand \left(7y\right)^{2}.
4x^{2}-49y^{2}+\left(x-7y\right)^{2}
Calculate 7 to the power of 2 and get 49.
4x^{2}-49y^{2}+x^{2}-14xy+49y^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-7y\right)^{2}.
5x^{2}-49y^{2}-14xy+49y^{2}
Combine 4x^{2} and x^{2} to get 5x^{2}.
5x^{2}-14xy
Combine -49y^{2} and 49y^{2} to get 0.
\left(2x\right)^{2}-\left(7y\right)^{2}+\left(x-7y\right)^{2}
Consider \left(2x+7y\right)\left(2x-7y\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
2^{2}x^{2}-\left(7y\right)^{2}+\left(x-7y\right)^{2}
Expand \left(2x\right)^{2}.
4x^{2}-\left(7y\right)^{2}+\left(x-7y\right)^{2}
Calculate 2 to the power of 2 and get 4.
4x^{2}-7^{2}y^{2}+\left(x-7y\right)^{2}
Expand \left(7y\right)^{2}.
4x^{2}-49y^{2}+\left(x-7y\right)^{2}
Calculate 7 to the power of 2 and get 49.
4x^{2}-49y^{2}+x^{2}-14xy+49y^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-7y\right)^{2}.
5x^{2}-49y^{2}-14xy+49y^{2}
Combine 4x^{2} and x^{2} to get 5x^{2}.
5x^{2}-14xy
Combine -49y^{2} and 49y^{2} to get 0.