Factor completely: $6c^2 - 6$
Understand the Problem
The question asks to completely factor the given expression, $6c^2 - 6$. The first step is to find the greatest common factor (GCF) of the terms, then factor it out. After that, determine if the resulting expression can be further factored, such as using the difference of squares.
Answer
$6(c-1)(c+1)$
Answer for screen readers
$6(c-1)(c+1)$
Steps to Solve
- Find the Greatest Common Factor (GCF)
The GCF of $6c^2$ and $-6$ is $6$.
- Factor out the GCF
Factoring out $6$ from the expression $6c^2 - 6$ gives us: $6(c^2 - 1)$
- Recognize the Difference of Squares
The expression $c^2 - 1$ is a difference of squares, since $c^2$ is a perfect square and $1$ is also a perfect square ($1 = 1^2$).
- Factor the Difference of Squares
The difference of squares $c^2 - 1$ can be factored as $(c - 1)(c + 1)$.
- Write the Completely Factored Expression
Substituting this back into the expression from step 2, we get the completely factored expression: $6(c - 1)(c + 1)$
$6(c-1)(c+1)$
More Information
The expression is now completely factored, meaning it cannot be factored any further.
Tips
A common mistake is to factor out the 6 but then forget to factor the resulting difference of squares. Another common mistake is not factoring out the GCF at all.
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