How do you factor $1/25h^2-16=0$ ?

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Answer 1 · 2015-05-09T04:41:54

To eliminate the fraction, we can multiply both sides of the equation by 25

$25(1/25h^2-16)=25*0$

$-> h^2 - 25*16 = 0$

$-> h^2 - 5^2*4^2 = 0$

$-> h^2 - (5*4)^2 = 0$

$-> h^2 - 20^2 = 0$

We know the Difference of Squares Identity which says:
$color(blue)(a^2 - b^2 = (a+b)(a-b)$

Applying it to the equation, we get:

$-> color(green)((h+20)(h-20) = 0$

This tells us that either $h+20 = 0$ or $h-20 = 0$

$color(green)(h = -20 or h = 20$

How do you factor 1/25h^2-16=01/25h^2-16=0?