factorise

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February 24th 2010, 09:34 PM
Tessarina

factorise

please fully factorise:

49-(x-4)^2
February 24th 2010, 09:47 PM
drewbear

$49-(x-4)^2$

$<br /> 49-(x-4)(x-4)<br />$

$<br /> 49-(x^2-8x+16)<br />$

$<br /> 49-x^2+8x-16<br />$

$<br /> -x^2+8x+33<br />$

$<br /> (-x+11)(x+3)<br />$
February 25th 2010, 01:27 AM
HallsofIvy

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 $(x-4)^2$ .

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

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