SOLUTION: Multiply and simplify. [ (5t^3)/(4t � 8) ] [ (6t

SOLUTION: Multiply and simplify. [ (5t^3)/(4t � 8) ] [ (6t - 12) / (10t) ]

Question 215685This question is from textbook Intermediate Algebra
: Multiply and simplify.
[ (5t^3)/(4t � 8) ] [ (6t - 12) / (10t) ]
This question is from textbook Intermediate Algebra

Found 2 solutions by stanbon, jsmallt9:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Multiply and simplify.
[ (5t^3)/(4t � 8) ] [ (6t - 12) / (10t) ]
---------------------
Factor where you can:
[ (5t^3)/(4(t � 2) ] [ (6(t - 2) / (10t) ]
-----------
Cancel factors common to numerator and denominator
such as, (t-2), 5, t, 2, to get:
---
[ (t^2)/4] [ (6/ (2) ]
---
Cancel the "2" again to get:
= (3/4)t^2
==================
Cheers,
Stan H.
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

Way back when you first started multiplying fractions, before you even knew about variables, you learned that one could "cross cancel" common factors before multiplying and that doing so often made the multiplication easier. This is still true, even though we now have variables, exponenets and multiple term numerators and denominators. The part that is harder is finding the common factors.

So we want to start by expressing each numerator and denominator as a product (aka multiplication). In other words, we want to factor each numerator and denominator, hoping to find common factors to cancel.
The first numerator and second denominator are already products. So we'll focus on the first denominator and second numerator. As usual, start with Greatest Common Factor (GCF):

We can see that we already have some common factors to cancel. But before doing so, I am going to factor some of the monomial (single term) factors to make all the common factors visible:

Now we can cross cancel:

leaving

Now we have a simple multiplication which results in:

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