Step 1: Understanding the Expression
To multiply the expressions (3/4x - 4/3y) and (2/3x + 3/2y), we will use the distributive property. This involves multiplying each term in the first expression by each term in the second expression.
Step 2: Applying the Distributive Property
- First, multiply 3/4x by each term in the second expression:
- (3/4x) * (2/3x) = 3 * 2 / (4 * 3) * x^2 = 6/12x^2 = 1/2x^2
- (3/4x) * (3/2y) = 3 * 3 / (4 * 2) * xy = 9/8xy
- Next, multiply -4/3y by each term in the second expression:
- (-4/3y) * (2/3x) = -4 * 2 / (3 * 3) * xy = -8/9xy
- (-4/3y) * (3/2y) = -4 * 3 / (3 * 2) * y^2 = -6y^2
Step 3: Combining Like Terms
Now, we combine the results from the multiplication:
- From the first part: 1/2x^2 + 9/8xy
- From the second part: -8/9xy - 6y^2
Combining the like terms (xy):
Step 4: Final Expression
- Combine the xy terms:
- 9/8xy - 8/9xy
- To combine these, find a common denominator (72):
- (9/8) * (9/9) = 81/72
- (-8/9) * (8/8) = -64/72
- The combined term = 81/72 - 64/72 = 17/72xy
The final result of the multiplication is:
Result: 1/2x^2 + 17/72xy - 6y^2