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#