(3a%2B2)%2B4(a-2).jpeg "(2a-1)(3a+2)+4(a-2)")
Expanding and Simplifying the Expression (2a-1)(3a+2)+4(a-2)
This article will guide you through the process of expanding and simplifying the algebraic expression (2a-1)(3a+2)+4(a-2).
Step 1: Expanding the First Part
We start by expanding the product of the two binomials: (2a-1)(3a+2). This can be done using the FOIL method (First, Outer, Inner, Last):
- First: 2a * 3a = 6a²
- Outer: 2a * 2 = 4a
- Inner: -1 * 3a = -3a
- Last: -1 * 2 = -2
Combining these terms, we get: 6a² + 4a - 3a - 2 = 6a² + a - 2
Step 2: Expanding the Second Part
Next, we expand the term 4(a-2) by distributing the 4:
4 * a = 4a 4 * -2 = -8
This gives us: 4a - 8
Step 3: Combining Terms
Now, we combine the results from steps 1 and 2:
(6a² + a - 2) + (4a - 8)
This simplifies to: 6a² + 5a - 10
Conclusion
Therefore, the simplified form of the expression (2a-1)(3a+2)+4(a-2) is 6a² + 5a - 10.