How do you multiply #(8x^2)/(x^2-9)*(x^2+6x+9)/(16x^3)#?

1 Answer
Mar 7, 2016

Answer:

#=((x+3)) / (2x^2 - 6x) #

Explanation:

#(8x^2)/(x^2-9) * (x^2 +6x +9) / (16x^3)#

1. Factorising #(x^2 +6x +9)#

We can Split the Middle Term of this expression to factorise it.

#(x^2 +6x +9) = x^2 +3x +3x+9= x (x+3) + 3 (x+3)= color(purple)((x+3) *(x+3)#

2. Factorising #(x^2-9)#:
The above expression is of the form #a^2 - b^2 = (a+b)(a-b)#
So,#(x^2-9) = (x^2 -3^2) = color(blue)((x+3)(x-3)#

The expression now becomes:
#((8x^2)/(color(blue)((x+3)(x-3))))* (color(purple)((x+3) *(x+3)) / (16x^3))#

#=((8x^2)/(color(blue)(cancel((x+3))(x-3))))* (color(purple)(cancel((x+3)) *(x+3)) / (16x^3))#

#=((8x^2)/((x-3))* ((x+3)) / (16x^3))#

#=(cancel(8x^2)/((x-3))* ((x+3)) / (cancel(16x^3)))#

#=((x+3)) / ((x-3) *(2x)#

#=((x+3)) / (2x * (x) + 2x * (-3) #

#=((x+3)) / (2x^2 - 6x) #