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

Question

Genesis Allen · Accepted Answer

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

#(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) #

Savannah Anderson · Answer

undefined To multiply the given expression, you can follow these steps:

1. Simplify each expression separately:
   - Simplify (8x^2)/(x^2-9) by factoring the denominator as (x+3)(x-3) and canceling common factors.
   - Simplify (x^2+6x+9)/(16x^3) by factoring the numerator as (x+3)(x+3) and canceling common factors.

2. Multiply the simplified expressions together by multiplying the numerators and denominators separately.

3. Combine like terms and simplify the resulting expression, if possible.

The final expression will be the result of multiplying the given expression.