How do you simplify #(5y+3)(5y-3)(25y^2+9)#?

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Answer 1 · 2015-06-22T06:39:07

#(5y+3)(5y-3)(25y^2+9) = (25y^2-9)(25y^2+9) = 625y^4-81#

This uses the difference of squares identity twice:

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

#(5y+3)(5y-3)(25y^2+9)#

#= ((5y)^2-3^2)(25y^2+9)#

#= (25y^2-9)(25y^2+9)#

#= ((25y^2)^2-9^2)#

#= 625y^4-81#