Range: difference between the highest and lowest values
First order from smallest to greatest
3, 8, 24, 24, 29, 38, 62
Smallest number: 3
Largest number: 62
62 - 3 = 59
Solution: the range is 59

7 0

3 years ago

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

yarga [219]

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

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

$(5x+7)^3$

4 0

3 years ago

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