\[{(4a-3b)}^{2}\]
1
Use Square of Difference: (a−b)2=a2−2ab+b2{(a-b)}^{2}={a}^{2}-2ab+{b}^{2}.
(4a)2−2×4a×3b+(3b)2{(4a)}^{2}-2\times 4a\times 3b+{(3b)}^{2}

2
Use Multiplication Distributive Property: (xy)a=xaya{(xy)}^{a}={x}^{a}{y}^{a}.
42a2−2×4a×3b+(3b)2{4}^{2}{a}^{2}-2\times 4a\times 3b+{(3b)}^{2}

3
Simplify  42{4}^{2}  to  1616.
16a2−2×4a×3b+(3b)216{a}^{2}-2\times 4a\times 3b+{(3b)}^{2}

4
Use Multiplication Distributive Property: (xy)a=xaya{(xy)}^{a}={x}^{a}{y}^{a}.
16a2−2×4a×3b+32b216{a}^{2}-2\times 4a\times 3b+{3}^{2}{b}^{2}

5
Simplify  32{3}^{2}  to  99.
16a2−2×4a×3b+9b216{a}^{2}-2\times 4a\times 3b+9{b}^{2}

6
Simplify  2×4a×3b2\times 4a\times 3b  to  24ab24ab.
16a2−24ab+9b216{a}^{2}-24ab+9{b}^{2}

Done
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