How do you multiply #(3x-8)(3x+8)#?

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Answer 1 · 2016-07-30T16:47:00

#9x^2-64#

#color(blue)("A bit of a cheat approach.")#

Known that #a^2-b^2" "=" "(a-b)(a+b)#

We have the same equation structure in #(3x-8)(3x+8)#
So we know that this is the same as:

#[(3x)^2-(8)^2] = 9x^2-64#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Doing it the hard way")#

We have #color(blue)((3x-8))color(brown)((3x+8))#

Multiply everything in the brown brackets by everything in the blue brackets.

#color(brown)(color(blue)(3x)(3x+8)color(blue)(" "-8)(3x+8))#

#9x^2+24x" "-24x-64#

But #" "24x-24x=0# giving

#9x^2-64#