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Ipatiy [6.2K]
2 years ago
5

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

Mathematics
2 answers:
lutik1710 [3]2 years ago
5 0

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
yarga [219]2 years ago
4 0

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

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