please fully factorise:

49-(x-4)^2

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- Feb 24th 2010, 09:34 PMTessarinafactorise
please fully factorise:

49-(x-4)^2 - Feb 24th 2010, 09:47 PMdrewbear
$\displaystyle 49-(x-4)^2$

$\displaystyle

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

$

$\displaystyle

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

$

$\displaystyle

49-x^2+8x-16

$

$\displaystyle

-x^2+8x+33

$

$\displaystyle

(-x+11)(x+3)

$ - Feb 25th 2010, 01:27 AMHallsofIvy
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: $\displaystyle a^2- b^2= (a- b)(a+ b)$.

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

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