Question

What is the factored form of the binomial expansion 125x^3 + 525x^2 + 735x + 343?

Answer 1

Answer:

(5x+7)^3

Step-by-step explanation:

(a+b)^3=a^3+3a^2b+3ab^2+b^3

• 125x^3 + 525x^2 + 735x + 343=
• (5x)^3+3*(5x)^2*7+3*5x*7^2+7^3=
• (5x+7)^3

Answer 2

Answer:

Step-by-step explanation:

1. regroup terms

$125x^3+343+525x^2+735x$

2. Rewrite $125x^3$ as  $(5x)^3$ and 343 as $7^3$

$(5x)^3+7^3+525x^2+735x$

3. Since both terms are perfect cubes, factor using the sum of cubes formula, $a^3+b^3 = (a+b)(a^2-ab+b^2)$, where $a=5x$ and $b=7$

$(5x+7)((5x)^2-(7)(5x)+(7)^2)+525x^2+735x$

$(5x+7)(25x^2-35x+49)+525x^2+735x$

4. Factor $105x$ out of $525x^2+735x$

$(5x+7)(25x^2-35x+49)+105x(5x+7)$

5. Regroup

$(5x+7)(25x^2-35x+49+105x)$

$(5x+7)(25x^2+70x+49)$

6. Factor again

$(5x+7)(5x+7)^2$

$(5x+7)^3$