How do you factor #8 - 2b - b^2#?

1 Answer

Answer:

# color(green)(-1(b-2)(b+4)# is the factorised format.

Explanation:

#8 - 2b - b^2 =- (b^2 + 2b -8) #

We can Split the Middle Term of #b^2 + 2b -8# to factorise it.

In this technique, if we have to factorise an expression like #ax^2 + bx + c#, we need to think of 2 numbers such that:

#N_1*N_2 = a*c = 1*-8 = -8#
and
#N_1 +N_2 = b = 2#
After trying out a few numbers we get #N_1 = 4# and #N_2 =-2#
#4*-2 = -8# and #4+(-2)= 2#

#b^2 + 2b -8 = b^2 + 4b - 2b -8 #
#= b(b+4) - 2(b+4)#
#b+4# is common to both terms:
# =color(green)( (b-2)(b+4)#