(3a-b)(2a%2B7b).jpeg "(a+b)(3a-b)(2a+7b)")
Expanding the Expression (a+b)(3a-b)(2a+7b)
This article will guide you through the process of expanding the given algebraic expression: (a+b)(3a-b)(2a+7b). We will use the distributive property (often referred to as FOIL) to break down the expression into simpler terms.
Step 1: Multiply the first two factors
First, let's expand the product of the first two factors: (a+b)(3a-b).
Using the distributive property (FOIL):
- First: a * 3a = 3a²
- Outer: a * -b = -ab
- Inner: b * 3a = 3ab
- Last: b * -b = -b²
Combining the terms, we get: 3a² - ab + 3ab - b² = 3a² + 2ab - b²
Step 2: Multiply the result by the third factor
Now, we have to multiply the result from Step 1, (3a² + 2ab - b²), by the third factor (2a+7b).
Again, applying the distributive property:
- (3a² + 2ab - b²) * 2a = 6a³ + 4a²b - 2ab²
- (3a² + 2ab - b²) * 7b = 21a²b + 14ab² - 7b³
Finally, combining all the terms, we get the expanded expression:
6a³ + 4a²b - 2ab² + 21a²b + 14ab² - 7b³ = 6a³ + 25a²b + 12ab² - 7b³
Conclusion
Therefore, the expanded form of the expression (a+b)(3a-b)(2a+7b) is 6a³ + 25a²b + 12ab² - 7b³. Remember, you can apply this same process to expand any similar expression involving multiple factors.