8x3−1258{x}^{3}-125
1
Rewrite it in the form a3−b3{a}^{3}-{b}^{3}, where a=2xa=2x and b=5b=5.
(2x)3−53{(2x)}^{3}-{5}^{3}

2
Use Difference of Cubes: a3−b3=(a−b)(a2+ab+b2){a}^{3}-{b}^{3}=(a-b)({a}^{2}+ab+{b}^{2}).
(2x−5)((2x)2+(2x)(5)+52)(2x-5)({(2x)}^{2}+(2x)(5)+{5}^{2})

3
Use Multiplication Distributive Property: (xy)a=xaya{(xy)}^{a}={x}^{a}{y}^{a}.
(2x−5)(22x2+2x×5+52)(2x-5)({2}^{2}{x}^{2}+2x\times 5+{5}^{2})

4
Simplify  22{2}^{2}  to  44.
(2x−5)(4x2+2x×5+52)(2x-5)(4{x}^{2}+2x\times 5+{5}^{2})

5
Simplify  52{5}^{2}  to  2525.
(2x−5)(4x2+2x×5+25)(2x-5)(4{x}^{2}+2x\times 5+25)

6
Simplify  2x×52x\times 5  to  10x10x.
(2x−5)(4x2+10x+25)(2x-5)(4{x}^{2}+10x+25)

Done
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