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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 1: Q 125. (page 39)

In the following exercises, evaluate each expression.
$3 x^{2} - 4 x y + 2 y^{2}$ when $x = - 2$ and $y = - 3$

Short Answer

Expert verified

The value is 6.

Step by step solution

01

Step 1. Given Information:

The given expression is $3 x^{2} - 4 x y + 2 y^{2}$ and the values of the variables are $x = - 2$ and $y = - 3$ .

02

Step 2. Substitute the values:

Substitute $- 2$ for $x$ and $- 3$ for $y$ into the given expression $3 x^{2} - 4 x y + 2 y^{2}$ .

$3 {(- 2)}^{2} - 4 (- 2) (- 3) + 2 {(- 3)}^{2}$

03

Step 3. Calculate the exponents:

The values of the exponents are ${(- 3)}^{2} = 9$ and ${(- 2)}^{2} = 4$ . Simplify the exponents in the obtained expression.

$3 路 4 - 4 (- 2) (- 3) + 2 路 9$

04

Step 4. Multiply:

Perform multiplication from left to right.

$\begin{array}{rcl} 3 路 4 - 4 (- 2) (- 3) + 2 路 9 & = & 12 - 4 路 6 + 18 \\ = & 12 - 24 + 18 \end{array}$

05

Step 5. Perform Subtraction:

Subtract 24 from 12 in the obtained expression.

$- 12 + 18$

06

Step 6. Perform Addition:

Add 18 and $- 12$ in the obtained expression.

$- 12 + 18 = 6$

07

Step 7. Conclusion:

The value obtained is 6.

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