How do you factor the expression #20 - 5(x-3)^2#?

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Answer 1 · 2015-12-20T18:30:55

Factor out a #5# and apply the difference of squares formula to find that
#20 - 5(x-3)^2= 5(x-1)(x-5)#

The difference of squares formula states that

#a^2 - b^2 = (a+b)(a-b)#

With this, we have

#20 - 5(x-3)^2 = 5(4 - (x-3)^2)#

#= 5(2^2 - (x-3)^2)#

#= 5(2+(x-3))(2-(x-3))#

#= 5(x-1)(x-5)#