Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
![The equation given is:
\[ g(x) = 4x^2 - 3x \]
The task is to find the expression for \( g(x + a) - g(x) \).
Begin by substituting \( x + a \) into the function \( g(x) \) to find \( g(x + a) \).
\[ g(x + a) = 4(x + a)^2 - 3(x + a) \]
Now, expand and simplify \( g(x + a) \):
1. \( 4(x + a)^2 = 4(x^2 + 2ax + a^2) = 4x^2 + 8ax + 4a^2 \)
2. \( -3(x + a) = -3x - 3a \)
Therefore,
\[ g(x + a) = 4x^2 + 8ax + 4a^2 - 3x - 3a \]
Now, calculate \( g(x + a) - g(x) \):
\[ g(x + a) - g(x) = (4x^2 + 8ax + 4a^2 - 3x - 3a) - (4x^2 - 3x) \]
Simplify the expression:
\[ 8ax + 4a^2 - 3a \]
Thus, the result for the expression \( g(x + a) - g(x) \) is:
\[ 8ax + 4a^2 - 3a \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fda625b26-af5c-4d40-b5ca-dba856450987%2Ffa9928c9-eed9-4894-a15d-59d1d81b5f0d%2Frhqzq71_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The equation given is:
\[ g(x) = 4x^2 - 3x \]
The task is to find the expression for \( g(x + a) - g(x) \).
Begin by substituting \( x + a \) into the function \( g(x) \) to find \( g(x + a) \).
\[ g(x + a) = 4(x + a)^2 - 3(x + a) \]
Now, expand and simplify \( g(x + a) \):
1. \( 4(x + a)^2 = 4(x^2 + 2ax + a^2) = 4x^2 + 8ax + 4a^2 \)
2. \( -3(x + a) = -3x - 3a \)
Therefore,
\[ g(x + a) = 4x^2 + 8ax + 4a^2 - 3x - 3a \]
Now, calculate \( g(x + a) - g(x) \):
\[ g(x + a) - g(x) = (4x^2 + 8ax + 4a^2 - 3x - 3a) - (4x^2 - 3x) \]
Simplify the expression:
\[ 8ax + 4a^2 - 3a \]
Thus, the result for the expression \( g(x + a) - g(x) \) is:
\[ 8ax + 4a^2 - 3a \]
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