## Algebra 1

Published by Prentice Hall

# Chapter 7 - Exponents and Exponential Functions - 7-3 Multipying Powers with the Same Base - Practice and Problem-Solving Exercises: 47

#### Answer

$6x^{3} + 2x^{2}$

#### Work Step by Step

The Area of a rectangle is the product of its length and breadth. Hence, Area = $2x$ X ($3x^{2} + x)$ By the distributive property, Area = $2x$ X $3x^{2}$ + $2x$ X $x$ Now, $2x$ X $3x^{2}$ = $2$ X $3$ X $x^{1+2}$ = $6x^{3}$ $2x$ X $x$ = $2x^{1+1}$ = $2x^{2}$ (Since the exponents are added while multiplying with the same base) Final result : Area = $6x^{3}$ + $2x^{2}$

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