(2a-1)(3a+2)+4(a-2)

2 min read Jun 16, 2024
(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.