Factor 4x² − 4
Worked out line by line the way a teacher would write it.
Answer
| Factored form | 4(x − 1)(x + 1) |
Step-by-step solution
4 steps-
1 Given4 x^{2} - 4
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2 Factor out the greatest common factor 4
4 divides every term, so it can be written once in front of a bracket. This is the distributive property used backwards: ab + ac = a(b + c).
4 \left(x^{2} - 1\right)Every term is divisible by 4.
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3 Difference of squares: a² − b² = (a − b)(a + b), with a = x and b = 1
(a − b)(a + b) = a² − ab + ab − b² = a² − b², because the middle terms cancel. So any square minus a square factors this way.
\left(x - 1\right) \left(x + 1\right) -
4 Fully factored form4 \left(x - 1\right) \left(x + 1\right)
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