Q. \(x^2 – 25\)
Answer
We solve the equation by factoring the difference of squares:
\[
x^2 – 25 = (x-5)(x+5) = 0
\]
So:
\[
x-5=0 \Rightarrow x=5,\quad x+5=0 \Rightarrow x=-5
\]
Final result: \(x=5\) or \(x=-5\).
Detailed Explanation
We want to simplify the expression \(x^2 – 25\).
Step 1: Recognize a difference of squares.
The expression \(x^2 – 25\) matches the pattern
\[
a^2 – b^2
\]
where \(a = x\) and \(b = 5\), because \(25 = 5^2\).
Step 2: Use the factoring formula.
The key identity is
\[
a^2 – b^2 = (a – b)(a + b)
\]
Substitute \(a = x\) and \(b = 5\).
Step 3: Factor the expression.
\[
x^2 – 25 = x^2 – 5^2 = (x – 5)(x + 5)
\]
This is the factored form.
Final Answer:
\[
x^2 – 25 = (x – 5)(x + 5)
\]
See full solution
Graph
Algebra FAQ
What are the factors of \(x^2-25\)?
\(x^2-25=(x-5)(x+5)\).
Solve \(x^2-25=0\).
\(x^2=25\), so \(x=\pm 5\).
How do you use the difference of squares for \(x^2-25\)?
Recognize \(x^2-a^2\). Here \(a=5\), so \((x-5)(x+5)\).
What is the vertex form or completing-square form of \(x^2-25\)?
\(x^2-25\) is already a quadratic with completed square: \((x)^2-25\).
What is the graph intercepts of \(y=x^2-25\)?
\(y\)-intercept: \(x=0\Rightarrow y=-25\). \(x\)-intercepts: \(x=\pm 5\).
What is \(x^2-25\) in factored form if \(x=3\)?
Evaluate \(3^2-25=9-25=-16\). Factored check: \((3-5)(3+5)=(-2)(8)=-16\).
Use AI tools to solve x²−25.
Practice and check answers fast.
Practice and check answers fast.
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