Chapter 7: Q. 7.129 (page 874)

Factor completely:
$250 m^{3} + 432$

Short Answer

Expert verified

The factored form is $2 (5 m + 6) (25 m^{2} - 30 m + 36)$ .

Step by step solution

Step 1. Given Information

We are given a polynomial $250 m^{3} + 432$ ,

We have to factor the given polynomial.

Step 2. Factoring the polynomial

Factoring out GCF $2$ , we get

$250 m^{3} + 432 = 2 (125 m^{3} + 216)$

The above expression can be written as,

role="math" $250 m^{3} + 432 = 2 ({(5 m)}^{3} + 6^{3})$

Using $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ , we get

$= 2 (5 m + 6) ({(5 m)}^{2} - 5 m \cdot 6 + 6^{2}) = 2 (5 m + 6) (25 m^{2} - 30 m + 36)$

Step 3. Checking the factors

Using $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ , we get

$2 (5 m + 6) (25 m^{2} - 30 m + 36) = 250 m^{3} + 432 2 ({(5 m)}^{3} + 6^{3}) = 250 m^{3} + 432 250 m^{3} + 432 = 250 m^{3} + 432 L H S = R H S$

Hence, the factors are correct.

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Factor completely:
$250 m^{3} + 432$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Factoring the polynomial

Step 3. Checking the factors

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Factor completely:250m3+432

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Factoring the polynomial

Step 3. Checking the factors

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Mechanics Maths

Discrete Mathematics

Statistics

Theoretical and Mathematical Physics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Factor completely:
$250 m^{3} + 432$