Multiply. Simplify your answer.
1. (3h^3 - 6h/10g^2) x (4g/g^2 - 2g)
(This is the correct expression. There is no typo.)
A: ?
2. (m^2 + m - 2/m^2 - 2m - 8) x (m^2 -8 + 16/3m -3)
(This the correct expression. There is no typo.)
A: ?
Same old parenthesis-free exposition. Surely by now you can factor the expressions and eliminate common factors.
Take a look at
http://www.wolframalpha.com/input/?i=%28%283h^3+-+6h%29%2F%2810g^2%29%29+*+%28%284g%29%2F%28g^2+-+2g%29+%29
and notice how the parentheses make things work.
wolframalpha.com is your friend. It can solve these problems, and has the added benefit of forcing you to correctly express you fractions.
To solve these multiplication problems and simplify the answers, we need to follow a few steps.
1. Distribute: Distribute the terms in the first expression and the terms in the second expression.
2. Combine like terms: Combine like terms in both expressions separately.
3. Multiply the numerators and denominators separately.
Let's walk through both problems.
Problem 1:
(3h^3 - 6h/10g^2) x (4g/g^2 - 2g)
Step 1: Distribute
(3h^3 - 6h/10g^2) x (4g/g^2 - 2g)
= (3h^3 - 6h) x (4g/g^2 - 2g)
Step 2: Combine like terms
No like terms to combine in this expression.
Step 3: Multiply the numerators and denominators separately
(3h^3) x (4g) = 12h^3g
(-6h) x (4g) = -24hg
(3h^3) x (-2g) = -6h^3g
(-6h) x (-2g) = 12hg
Now we have:
(12h^3g - 24hg) / (10g^2 x g^2 - 2g x 10g^2)
Simplifying further:
(12h^3g - 24hg) / (10g^4 - 20g^3)
= (12h^3g - 24hg) / (10g^3(g - 2))
Problem 2:
(m^2 + m - 2/m^2 - 2m - 8) x (m^2 -8 + 16/3m -3)
Step 1: Distribute
(m^2 + m - 2/m^2 - 2m - 8) x (m^2 -8 + 16/3m - 3)
= (m^2 + m - 2) x (m^2 -8) + (m^2 + m - 2) x (16/3m - 3)
Step 2: Combine like terms
No like terms to combine in the first expression.
In the second expression, we have: (1/3)(16m - 48) = (16m/3 - 16)
Step 3: Multiply the numerators and denominators separately
(m^2) x (m^2) = m^4
(m^2) x (-8) = -8m^2
(m^2) x (16m/3) = (16m^3/3)
(m^2) x (-16) = -16m^2
(m^2) x (16) = 16m^2
(m^2) x (16/3m) = (16m^3/3)
(m^2) x (-3) = -3m^2
(m^2) x (16m/3) = (16m^3/3)
(m^2) x (-16/3) = (-16m^2/3)
Now we have:
(m^4 - 8m^2 + 16m^3/3 - 16m^2) / (m^2 - 2m - 8)
Simplifying further:
(m^4 + 16m^3/3 - 24m^2) / (m^2 - 2m - 8)
This is the simplified answer for problem 2.