How do you factor #a^2+8a-48#?

1 Answer
George C.
Feb 11, 2017

#a^2+8a-48 = (a-4)(a+12)#

Explanation:

The difference of squares identity can be written:

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

Complete the square and use this with #A=(a+4)# and #B=8# as follows:

#a^2+8a-48 = a^2+8x+16-64#

#color(white)(a^2+8a-48) = (a+4)^2-8^2#

#color(white)(a^2+8a-48) = ((a+4)-8)((a+4)+8)#

#color(white)(a^2+8a-48) = (a-4)(a+12)#

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