(2x−1)3{(2x-1)}^{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}.
(2x−1)((2x)2−2×2x+1)(2x-1)({(2x)}^{2}-2\times 2x+1)

2
Use Multiplication Distributive Property: (xy)a=xaya{(xy)}^{a}={x}^{a}{y}^{a}.
(2x−1)(22x2−2×2x+1)(2x-1)({2}^{2}{x}^{2}-2\times 2x+1)

3
Simplify  22{2}^{2}  to  44.
(2x−1)(4x2−2×2x+1)(2x-1)(4{x}^{2}-2\times 2x+1)

4
Simplify  2×2x2\times 2x  to  4x4x.
(2x−1)(4x2−4x+1)(2x-1)(4{x}^{2}-4x+1)

5
Expand by distributing sum groups.
2x(4x2−4x+1)−(4x2−4x+1)2x(4{x}^{2}-4x+1)-(4{x}^{2}-4x+1)

6
Expand by distributing terms.
8x3−8x2+2x−(4x2−4x+1)8{x}^{3}-8{x}^{2}+2x-(4{x}^{2}-4x+1)

7
Remove parentheses.
8x3−8x2+2x−4x2+4x−18{x}^{3}-8{x}^{2}+2x-4{x}^{2}+4x-1

8
Collect like terms.
8x3+(−8x2−4x2)+(2x+4x)−18{x}^{3}+(-8{x}^{2}-4{x}^{2})+(2x+4x)-1

9
Simplify.
8x3−12x2+6x−18{x}^{3}-12{x}^{2}+6x-1

Done
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