Answer:
Step-by-step explanation:
1. regroup terms
[tex]125x^3+343+525x^2+735x[/tex]
2. Rewrite [tex]125x^3[/tex] as [tex](5x)^3[/tex] and 343 as [tex]7^3[/tex]
[tex](5x)^3+7^3+525x^2+735x[/tex]
3. Since both terms are perfect cubes, factor using the sum of cubes formula, [tex]a^3+b^3 = (a+b)(a^2-ab+b^2)[/tex], where [tex]a=5x[/tex] and [tex]b=7[/tex]
[tex](5x+7)((5x)^2-(7)(5x)+(7)^2)+525x^2+735x[/tex]
[tex](5x+7)(25x^2-35x+49)+525x^2+735x[/tex]
4. Factor [tex]105x[/tex] out of [tex]525x^2+735x[/tex]
[tex](5x+7)(25x^2-35x+49)+105x(5x+7)[/tex]
5. Regroup
[tex](5x+7)(25x^2-35x+49+105x)[/tex]
[tex](5x+7)(25x^2+70x+49)[/tex]
6. Factor again
[tex](5x+7)(5x+7)^2[/tex]
[tex](5x+7)^3[/tex]
Answer:
(5x+7)^3
Step-by-step explanation:
(a+b)^3=a^3+3a^2b+3ab^2+b^3
