How do you factor the expression $20 - 5(x-3)^2$ ?

Question

1233 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-12-20T18:30:55

Factor out a $5$ and apply the difference of squares formula to find that
$20 - 5(x-3)^2= 5(x-1)(x-5)$

The difference of squares formula states that

$a^2 - b^2 = (a+b)(a-b)$

With this, we have

$20 - 5(x-3)^2 = 5(4 - (x-3)^2)$

$= 5(2^2 - (x-3)^2)$

$= 5(2+(x-3))(2-(x-3))$

$= 5(x-1)(x-5)$

How do you factor the expression 20 - 5(x-3)^220 - 5(x-3)^2?