factor (m/4 + n/3)(3m/4 - 2n/3)
Is this the answer? if not, what did I do wrong? 3m^2/16 + mn/12 - 2n^2/9
First factor out the common denominator of 12²=144, which then gives automatically the factorization:
(3m+4n)(9m-8n)/144
It's already factored. If you wanted to expand it, your answer is correct.
To multiply two expressions, such as (m/4 + n/3) and (3m/4 - 2n/3), you need to apply the distributive property of multiplication over addition.
The correct way to multiply these two expressions is to multiply each term from the first expression by each term from the second expression:
(m/4 + n/3)(3m/4 - 2n/3) = (m/4)(3m/4) + (m/4)(-2n/3) + (n/3)(3m/4) + (n/3)(-2n/3)
Now let's simplify each term:
1. (m/4)(3m/4) = (3m^2/16)
2. (m/4)(-2n/3) = (-2mn/12)
3. (n/3)(3m/4) = (3mn/12)
4. (n/3)(-2n/3) = (-2n^2/9)
Now let's combine all the simplified terms:
(3m^2/16) + (-2mn/12) + (3mn/12) + (-2n^2/9)
Simplifying further, we can combine the middle terms: -2mn/12 + 3mn/12 = mn/12.
The final expression, after combining all the terms, is:
3m^2/16 + mn/12 - 2n^2/9
So, yes, your answer is correct! You did not do anything wrong.