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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 6.72 (page 1069)

Factor completely: $27 y^{2} - 48$

Short Answer

Expert verified

The required factors are $3 (3 y - 4) (3 y + 4)$

Step by step solution

01

Step 1. Given Information

The given expression is $27 y^{2} - 48$

02

Step 2. Calculation

We will first take out the common factor out and then apply the property to find the required factors.

$27 y^{2} - 48 = 3 (9 y^{2} - 16) = 3 ({(3 y)}^{2} - {(4)}^{2}) = 3 (3 y - 4) (3 y + 4)$

03

Step 3. Check

We will check the obtained factors by multiplying them.

$3 (3 y - 4) (3 y + 4) = 3 ({(3 y)}^{2} - {(4)}^{2}) = 27 y^{2} - 48$

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Most popular questions from this chapter

The number of hours it takes for ice to melt varies inversely with the air temperature. Suppose a block of ice melts in 2 hours when the temperature is 65 degrees Celsius.

Write the equation of variation.
How many hours would it take for the same block of ice to melt if the temperature was 78 degrees?

In the following exercises, factor.

$- 4 x^{3} y^{5} - x^{2} y^{3} + 12 x y^{4}$ .

In the following exercises, add or subtract $(1 + 3 i) + (7 + 4 i)$

In the following exercises, evaluate the function:

$a . g (h^{2}) b . g (x + 2) c . g (x) + g (2)$

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