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How do you find the product $(a - 3) (a + 3)$ $(a-3)(a+3)$ ?

1 Answer

Dec 26, 2016

$(a - 3) (a + 3) = a^{2} - 9$ $(a-3)(a+3)=color(green)(a^2-9)$

Explanation:

Either remember the general case
$XXX (p - q) (p + q) = p^{2} - q^{2}$ $color(white)("XXX")(p-q)(p+q)=p^2-q^2$ (sometimes called "the difference of squares")

...or do the multiplication
$(a - 3) (a + 3)$ $(a-3)(a+3)$
$XXX = (a - 3) a + (a - 3) 3$ $color(white)("XXX")=(a-3)a + (a-3)3$ (using the distributive property)

$XXX = (a^{2} - 3 a) + (3 a - 9)$ $color(white)("XXX")=(a^2-3a)+(3a-9)$

$XXX = a^{2} - 9$ $color(white)("XXX")=a^2-9$

(could also be done using FOIL or tabular multiplcation)

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