How do you factor #(b+2)^2 - (b-2)^2#?

1 Answer
Dec 6, 2015

Answer:

#8b#

Explanation:

#p^2 - q^2 = (p+q)(p-q)#

If #p = (b+2)# and #q = (b-2)#
Then the expression to be factored = #((b+2) + (b-2))((b+2) - (b-2))#
#= (2b)(4)#
=#8b#

This result can also be shown by simply expanding both square terms of the expression:

#(b^2 + 4b + 4) - (b^2 -4b + 4) = 8b#