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How do I decompose $x^2-9$ using the distributive property?
in Mathematics by Diamond (61,678 points) | 23 views

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It can also be said of an expression such as $x^2 − 9$ that it does not seem to match $xy + xz$. However, we can decompose the expression $x^2 − 9$ as shown below:

$x^2 − 9$

$= x^2 + 0x − 9$  (adding $0x$ to the expression $x^2 − 9$ does not change its value)

$= x^2 + 3x − 3x − 9$  ($+3x − 3x = 0; + 3x $ and $−3x$ are additive inverses)

$= x \cdot x + 3x − 3x + 3 \cdot 3$

$= x(x + 3) − 3(x + 3)$

$= (x + 3)(x − 3)$
by Diamond (61,678 points)

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