How do you factor #a^2-b^2+6b-9#?

1 Answer
May 19, 2017

Answer:

#a^2-b^2+6b-9 = (a-b+3)(a+b-3)#

Explanation:

The difference of squares identity can be written:

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

We can use this with #A=a# and #B=b-3# as follows:

#a^2-b^2+6b-9 = a^2-(b^2-6b+9)#

#color(white)(a^2-b^2+6b-9) = a^2-(b-3)^2#

#color(white)(a^2-b^2+6b-9) = (a-(b-3))(a+(b-3))#

#color(white)(a^2-b^2+6b-9) = (a-b+3)(a+b-3)#