Use Square of Sum: \({(a+b)}^{2}={a}^{2}+2ab+{b}^{2}\).
\[{(4x)}^{2}+2\times 4x\times 3y+{(3y)}^{2}-{(4x-3y)}^{2}-48xy\]
Use Square of Difference: \({(a-b)}^{2}={a}^{2}-2ab+{b}^{2}\).
\[{(4x)}^{2}+2\times 4x\times 3y+{(3y)}^{2}-({(4x)}^{2}-2\times 4x\times 3y+{(3y)}^{2})-48xy\]
Remove parentheses.
\[{(4x)}^{2}+2\times 4x\times 3y+{(3y)}^{2}-{(4x)}^{2}+2\times 4x\times 3y-{(3y)}^{2}-48xy\]
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[{4}^{2}{x}^{2}+2\times 4x\times 3y+{(3y)}^{2}-{4}^{2}{x}^{2}+2\times 4x\times 3y-{(3y)}^{2}-48xy\]
Simplify \({4}^{2}\) to \(16\).
\[16{x}^{2}+2\times 4x\times 3y+{(3y)}^{2}-16{x}^{2}+2\times 4x\times 3y-{(3y)}^{2}-48xy\]
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[16{x}^{2}+2\times 4x\times 3y+{3}^{2}{y}^{2}-16{x}^{2}+2\times 4x\times 3y-{3}^{2}{y}^{2}-48xy\]
Simplify \({3}^{2}\) to \(9\).
\[16{x}^{2}+2\times 4x\times 3y+9{y}^{2}-16{x}^{2}+2\times 4x\times 3y-9{y}^{2}-48xy\]
Simplify \(2\times 4x\times 3y\) to \(24xy\).
\[16{x}^{2}+24xy+9{y}^{2}-16{x}^{2}+24xy-9{y}^{2}-48xy\]
Collect like terms.
\[(16{x}^{2}-16{x}^{2})+(24xy+24xy-48xy)+(9{y}^{2}-9{y}^{2})\]
Simplify.
\[0\]
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