(x−4)3{(x-4)}^{3}
1
Use Cube of Difference: (a−b)3=a3−3a2b+3ab2−b3{(a-b)}^{3}={a}^{3}-3{a}^{2}b+3a{b}^{2}-{b}^{3}.
(x−4)(x2−2x×4+42)(x-4)({x}^{2}-2x\times 4+{4}^{2})

2
Simplify  42{4}^{2}  to  1616.
(x−4)(x2−2x×4+16)(x-4)({x}^{2}-2x\times 4+16)

3
Simplify  2x×42x\times 4  to  8x8x.
(x−4)(x2−8x+16)(x-4)({x}^{2}-8x+16)

4
Expand by distributing sum groups.
x(x2−8x+16)−4(x2−8x+16)x({x}^{2}-8x+16)-4({x}^{2}-8x+16)

5
Expand by distributing terms.
x3−8x2+16x−4(x2−8x+16){x}^{3}-8{x}^{2}+16x-4({x}^{2}-8x+16)

6
Expand by distributing terms.
x3−8x2+16x−(4x2−32x+64){x}^{3}-8{x}^{2}+16x-(4{x}^{2}-32x+64)

7
Remove parentheses.
x3−8x2+16x−4x2+32x−64{x}^{3}-8{x}^{2}+16x-4{x}^{2}+32x-64

8
Collect like terms.
x3+(−8x2−4x2)+(16x+32x)−64{x}^{3}+(-8{x}^{2}-4{x}^{2})+(16x+32x)-64

9
Simplify.
x3−12x2+48x−64{x}^{3}-12{x}^{2}+48x-64

Done
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