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:

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

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

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

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

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

$= 625y^4-81$

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