How do you factor $16 p^{2} - 36$ $16p^2-36$ ?

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How do you factor $16 p^{2} - 36$ $16p^2-36$ ?

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Answer 1 · 2016-03-20T10:53:38

4(2p - 3)(2p + 3 )

Explanation:

First 'take out' the common factor of 4.

$16 p^{2} - 36 = 4 (4 p^{2} - 9)$ $16p^2 - 36 = 4(4p^2 - 9)$

now $4 p^{2} - 9 is a difference of squares$ $4p^2 - 9" is a difference of squares "$

A difference of squares factors : $a^{2} - b^{2} = (a - b) (a + b)$ $a^2 - b^2 = (a-b)(a+b)$

For $4 p^{2} - 9, a = 2 p and b = 3$ $4p^2 - 9 , a = 2p " and " b = 3$

hence : $4 p^{2} - 9 = (2 p - 3) (2 p + 3)$ $4p^2 - 9 = (2p-3)(2p+3)$

$\Rightarrow 16 p^{2} - 36 = 4 (2 p - 3) (2 p + 3)$ $rArr 16p^2 - 36 = 4(2p-3)(2p+3)$

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How do you factor $16 p^{2} - 36$ $16p^2-36$ ?

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