How do you factor $x^2+6xy+9y^2-25$ ?

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Answer 1 · 2018-03-28T06:15:51

$x^2+6xy+9y^2-25 = (x+3y-5)(x+3y+5)$

Given:

$x^2+6xy+9y^2-25$

Note that both $x^2+6xy+9y^2 = (x+3y)^2$ and $25 = 5^2$ are perfect squares.

So the given polynomial will factor as a difference of squares:

$A^2-B^2 = (A-B)(A+B)$

with $A=x+3y$ and $B=5$ ...

$x^2+6xy+9y^2-25 = (x+3y)^2-5^2$

$color(white)(x^2+6xy+9y^2-25) = ((x+3y)-5)((x+3y)+5)$

$color(white)(x^2+6xy+9y^2-25) = (x+3y-5)(x+3y+5)$

How do you factor x^2+6xy+9y^2-25x^2+6xy+9y^2-25?