How do you multiply #(10w-8)/(w+2)*(3w^2-w-14)/(25w^2-16)#?

Question

Avery Alexander · Accepted Answer

#(6w -14)/(5w +4)#

#25w^2 -16# should be screaming "the difference of two squares" to you. #(5w -4)(5w +4)# So look to factorise the other terms:

#(2(5w -4))/(w +2)##xx# #((w +2)(3w -7))/((5w -4)(5w +4))#

Cancel down to leave

#2/1##xx##(3w -7)/(5w +4)#

#=># #(6w -14)/(5w +4)#

Isaiah Anthony · Answer

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

1. Factorize the numerator and denominator of each expression, if possible.
2. Cancel out any common factors between the numerators and denominators.
3. Multiply the remaining factors in the numerator and denominator.

Let's apply these steps to the given expressions:

Expression 1: (10w-8)/(w+2)
- The numerator cannot be factored further.
- The denominator cannot be factored further.

Expression 2: (3w^2-w-14)/(25w^2-16)
- The numerator cannot be factored further.
- The denominator is a difference of squares, so it can be factored as (5w+4)(5w-4).

Now, cancel out any common factors between the numerators and denominators:
- There are no common factors to cancel out.

Multiply the remaining factors in the numerator and denominator:
- Numerator: (10w-8)(3w^2-w-14)
- Denominator: (w+2)(5w+4)(5w-4)

Therefore, the multiplication of the given expressions is:
(10w-8)(3w^2-w-14) / (w+2)(5w+4)(5w-4)