(3a%2Bb)-(a%2Bb)(a%2B2b)%2B(a%2B2b)%5E2.jpeg "(a+2b)(3a+b)-(a+b)(a+2b)+(a+2b)^2")
Simplifying the Expression (a+2b)(3a+b)-(a+b)(a+2b)+(a+2b)^2
This article will guide you through simplifying the expression: (a+2b)(3a+b)-(a+b)(a+2b)+(a+2b)^2
Step 1: Expanding the Products
Let's begin by expanding each of the products in the expression:
- (a+2b)(3a+b) = 3a² + ab + 6ab + 2b² = 3a² + 7ab + 2b²
- (a+b)(a+2b) = a² + 2ab + ab + 2b² = a² + 3ab + 2b²
- (a+2b)² = (a+2b)(a+2b) = a² + 2ab + 2ab + 4b² = a² + 4ab + 4b²
Step 2: Substituting the Expanded Products
Now, substitute the expanded products back into the original expression:
(3a² + 7ab + 2b²) - (a² + 3ab + 2b²) + (a² + 4ab + 4b²)
Step 3: Combining Like Terms
Finally, combine the like terms to simplify the expression:
3a² + 7ab + 2b² - a² - 3ab - 2b² + a² + 4ab + 4b² = 3a² - a² + a² + 7ab - 3ab + 4ab + 2b² - 2b² + 4b² = 3a² + 8ab + 4b²
Conclusion
Therefore, the simplified form of the expression (a+2b)(3a+b)-(a+b)(a+2b)+(a+2b)^2 is 3a² + 8ab + 4b².