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\left(3x\right)^{2}-\left(4y\right)^{2}
Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
3^{2}x^{2}-\left(4y\right)^{2}
Expand \left(3x\right)^{2}.
9x^{2}-\left(4y\right)^{2}
Calculate 3 to the power of 2 and get 9.
9x^{2}-4^{2}y^{2}
Expand \left(4y\right)^{2}.
9x^{2}-16y^{2}
Calculate 4 to the power of 2 and get 16.
\left(3x\right)^{2}-\left(4y\right)^{2}
Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
3^{2}x^{2}-\left(4y\right)^{2}
Expand \left(3x\right)^{2}.
9x^{2}-\left(4y\right)^{2}
Calculate 3 to the power of 2 and get 9.
9x^{2}-4^{2}y^{2}
Expand \left(4y\right)^{2}.
9x^{2}-16y^{2}
Calculate 4 to the power of 2 and get 16.