# Math Help - factorise

1. ## factorise

49-(x-4)^2

2. $49-(x-4)^2$

$
49-(x-4)(x-4)
$

$
49-(x^2-8x+16)
$

$
49-x^2+8x-16
$

$
-x^2+8x+33
$

$
(-x+11)(x+3)
$

3. But why in the world would you multiply something you want to factor?

Tessarina, one of the easiest factoring formulas is the "difference of squares" formula: $a^2- b^2= (a- b)(a+ b)$.

Here, $a^2= 49= 7^2$ and $(x-4)^2$.

$49- (x-4)^2= (7- (x-4))(7+ (x-4))= (11- x)(3+ x)$.