How do you factor completely 2a^2 - 4a - 2?

1 Answer
Oct 28, 2016

2a^2-4a-2 = 2(a-1-sqrt(3))(a-1+sqrt(3))

Explanation:

The difference of squares identity can be written:

A^2-B^2 = (A-B)(A+B)

Use this with A=(a-1) and B=sqrt(3) as follows:

2a^2-4a-2 = 2(a^2-2a-2)

color(white)(2a^2-4a-2) = 2(a^2-2a+1-3)

color(white)(2a^2-4a-2) = 2((a-1)^2-(sqrt(3))^2)

color(white)(2a^2-4a-2) = 2((a-1)-sqrt(3))((a-1)+sqrt(3))

color(white)(2a^2-4a-2) = 2(a-1-sqrt(3))(a-1+sqrt(3))