(b%2B2)%3D.jpeg "(3b-4)(b+2)=")
Expanding the Expression: (3b-4)(b+2)
This article will guide you through the process of expanding the algebraic expression (3b-4)(b+2).
Understanding the Process
Expanding this expression involves using the distributive property. The distributive property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products.
Applying the Distributive Property
-
First, multiply the first term of the first binomial (3b) by each term of the second binomial (b + 2):
- (3b)(b) = 3b²
- (3b)(2) = 6b
-
Next, multiply the second term of the first binomial (-4) by each term of the second binomial (b + 2):
- (-4)(b) = -4b
- (-4)(2) = -8
-
Now, combine all the terms:
- 3b² + 6b - 4b - 8
-
Finally, simplify by combining like terms:
- 3b² + 2b - 8
The Expanded Expression
Therefore, the expanded form of (3b-4)(b+2) is 3b² + 2b - 8.
Conclusion
By applying the distributive property, we successfully expanded the given expression. This process is crucial for solving algebraic equations and simplifying complex expressions.