Q. \[ (x+4)(x-4) \]
Answer
Expand using the distributive property:
\[
(x+4)(x-4)=x(x-4)+4(x-4)=x^2-4x+4x-16=x^2-16.
\]
Final result:
\[
x^2-16.
\]
Detailed Explanation
We want to simplify the product \((x+4)(x-4)\).
Step 1: Recognize the structure
This expression matches the difference of squares pattern.
The difference of squares identity is:
\[
(a+b)(a-b)=a^2-b^2
\]
Step 2: Identify \(a\) and \(b\)
Compare \((x+4)(x-4)\) with \((a+b)(a-b)\).
We have:
\[
a=x,\quad b=4
\]
Step 3: Apply the identity
Substitute \(a=x\) and \(b=4\) into the formula \(a^2-b^2\):
\[
(x+4)(x-4)=x^2-4^2
\]
Step 4: Compute \(4^2\)
\[
4^2=16
\]
Step 5: Write the final simplified result
\[
(x+4)(x-4)=x^2-16
\]
See full solution
Graph
Algebra FAQ
What is \( (x+4)(x-4) \) simplified?
\[\,(x+4)(x-4)=x^2-16.\]
Can this be recognized as a difference of squares?
Yes. Use \( (a+b)(a-b)=a^2-b^2 \) with \(a=x\), \(b=4\), giving \(x^2-16\).
What is the expanded form of \( (x+4)(x-4) \)?
Distribute: \(x(x-4)+4(x-4)=x^2-4x+4x-16=x^2-16\).
If \( (x+4)(x-4)=0 \), what are the solutions for \(x\)?
Set factors to zero: \(x+4=0\) so \(x=-4\), and \(x-4=0\) so \(x=4\).
What is the y-intercept when the expression is viewed as a function of \(x\)?
Evaluate at \(x=0\): \((0+4)(0-4)=4\cdot(-4)=-16\).
Is \( (x+4)(x-4) \) always nonnegative?
No. It equals \(x^2-16\), which is negative for \(-4<x<4\) and nonnegative for \(|x|\ge 4\).
Use AI tools to solve (x+4)(x-4).
Check steps, simplify, and verify.
Check steps, simplify, and verify.
298,376+ active customers
Math, Geometry, Trigonometry, etc.
Math, Geometry, Trigonometry, etc.
Unlimited AI homework help 
Diagram Generator, Flashcard Maker, Notes Generator, Research Assistant, Answer Generator, AI Homework Helper & AI Detector