(2a%2B3b)(2x-y).jpeg "(a+b)(2a+3b)(2x-y)")
Expanding the Expression (a+b)(2a+3b)(2x-y)
This article will guide you through expanding the expression (a+b)(2a+3b)(2x-y) step-by-step.
Step 1: Expanding the first two factors
We start by expanding the first two factors, (a+b)(2a+3b):
-
FOIL method:
- First: a * 2a = 2a²
- Outer: a * 3b = 3ab
- Inner: b * 2a = 2ab
- Last: b * 3b = 3b²
-
Combining like terms, we get: 2a² + 5ab + 3b²
Step 2: Expanding the result with the third factor
Now, we multiply the result from step 1 with the third factor, (2x-y):
-
(2a² + 5ab + 3b²) * (2x-y)
-
Distribute the first term:
- 2a² * (2x-y) = 4a²x - 2a²y
-
Distribute the second term:
- 5ab * (2x-y) = 10abx - 5aby
-
Distribute the third term:
- 3b² * (2x-y) = 6b²x - 3b²y
Step 3: Combining all terms
Finally, we combine all the terms obtained in step 2:
4a²x - 2a²y + 10abx - 5aby + 6b²x - 3b²y
Final Result
The expanded form of (a+b)(2a+3b)(2x-y) is: 4a²x - 2a²y + 10abx - 5aby + 6b²x - 3b²y.