Determine g(x+a)−g(x)
 for the following function.

g(x)=4x2−4

To determine \( g(x + a) - g(x) \) for the given function \( g(x) = 4x^2 - 4 \), we need to follow these steps:

1. **Compute \( g(x + a) \):**
   Substitute \( x + a \) into the function:

\[
g(x + a) = 4(x + a)^2 - 4
\]

Expand the squared term:

\[
(x + a)^2 = x^2 + 2ax + a^2
\]

So,

\[
g(x + a) = 4(x^2 + 2ax + a^2) - 4 = 4x^2 + 8ax + 4a^2 - 4
\]

2. **Subtract \( g(x) \) from \( g(x + a) \):**

\[
g(x + a) - g(x) = (4x^2 + 8ax + 4a^2 - 4) - (4x^2 - 4)
\]

Simplify by canceling like terms:

\[
g(x + a) - g(x) = 8ax + 4a^2
\]

### Final Answer:

\[
g(x + a) - g(x) = 8ax + 4a^2
\]

Would you like further details on any step, or have any questions?

### Related Questions:
1. How would you solve for \( g(x + 2a) - g(x) \) given the same function?
2. What is the derivative of \( g(x) = 4x^2 - 4 \)?
3. How can you interpret the result \( 8ax + 4a^2 \) in terms of algebraic functions?
4. How would the expression change if \( g(x) = 4x^2 - 4x + 1 \)?
5. What is the second derivative of \( g(x) = 4x^2 - 4 \)?

### Tip:
Always double-check the expansion of squared binomials to avoid common algebraic mistakes!

Determine g(x+a)−g(x) for the following function. g(x)=4x^2−4

Explore how to solve the algebraic problem g(x + a) - g(x) for the quadratic function g(x) = 4x^2 - 4. This step-by-step solution covers binomial expansion and simplifying quadratic expressions. Ideal for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation