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Ipatiy [6.2K]
3 years ago
5

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

Mathematics
2 answers:
lutik1710 [3]3 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]3 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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3 0
3 years ago
<img src="https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7B875%7D%20" id="TexFormula1" title=" \sqrt[3]{875} " alt=" \sqrt[3]{875} "
icang [17]

We are given the following expression:

\sqrt[3]{875}

We can factor 875 as:

\sqrt[3]{125\times7}

Now we will use the following property:

\sqrt[x]{a\times b}=\sqrt[x]{a}\times\sqrt[x]{b}

Applying the property:

\sqrt[3]{125}\times\sqrt[3]{7}

Solving the cubic root on the left:

5\sqrt[3]{7}

Since we get simplify any further this is the answer.

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11 months ago
1,3,1,9,1,27,1 identify a pattern in the given list of numbers
Bezzdna [24]
There is a one ever other number?
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3 years ago
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What is the value of x?<br> A. 25°<br> B. 50°<br> C. 55°<br> D. 75°<br> E. 80°
Troyanec [42]

Answer:

<h2><em><u>Option</u></em><em><u> </u></em><em><u>B</u></em></h2><h2><em><u>x</u></em><em><u> </u></em><em><u>=</u></em><em><u> </u></em><em><u>50</u></em><em><u>°</u></em><em><u> </u></em></h2>

Step-by-step explanation:

<em><u>By</u></em><em><u> </u></em><em><u>the</u></em><em><u> </u></em><em><u>condition</u></em><em><u>, </u></em>

25° + 105° + x = 180° <em>[</em><em>Angle</em><em> </em><em>sum</em><em> </em><em>property</em><em> </em><em>of</em><em> </em><em>triangle</em><em>]</em>

=> 130 + x = 180

=> x = 180 - 130

=> <em><u>x</u></em><em><u> </u></em><em><u>=</u></em><em><u> </u></em><em><u>50</u></em><em><u>°</u></em><em><u> </u></em><em><u>(</u></em><em><u>Ans</u></em><em><u>)</u></em>

6 0
3 years ago
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:)no characters needed just :)
mojhsa [17]

:)  :)  :)  :)  :)         :)  :)  :)  :)  :)

    :)  :)  :)                :)  :)  :)

         :)                     :)

            :)  :)  :)  :)  :)

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