How do you factor #144x²-81#?

2 Answers
May 23, 2016

This is of the form #a^2-b^2#, since both #144# and #81# are squares

Explanation:

We can even take out #9# and still have squares:
#=9xx16x^2-9xx3^2=9(16x^2-9)#

#=9(4^2xxx^2-3^2)=9((4x)^2-3^2)#

Since #a^2-b^2harr(a+b)(a-b)#:

#=9(4x+3)(4x-3)#

May 23, 2016

#9(4x-3)(4x+3)#

Explanation:

#9(16x^2-9)#

This can then be simplified to:

#9(4x-3)(4x+3)# using the difference of two squares rule.

Therefore, #x=±3/4#

Or, you could solve for #x# like this:

#144x^2-81#

#144x^2=81#

#x^2=81/144#

#x=±sqrt(81/144)#

#x= 3/4#

#x=-3/4#