(a%2Bb%2B2)-(a%2Bb)(a%2B3b%2B2).jpeg "(a+3b)(a+b+2)-(a+b)(a+3b+2)")
Simplifying the Expression: (a+3b)(a+b+2)-(a+b)(a+3b+2)
This article will guide you through the process of simplifying the given algebraic expression:
(a+3b)(a+b+2)-(a+b)(a+3b+2)
Step 1: Expand the Expressions
We begin by expanding both of the products using the distributive property (also known as FOIL):
- (a+3b)(a+b+2) = a(a+b+2) + 3b(a+b+2)
- (a+b)(a+3b+2) = a(a+3b+2) + b(a+3b+2)
Step 2: Distribute and Simplify
Let's distribute the terms and combine like terms:
- a(a+b+2) + 3b(a+b+2) = a² + ab + 2a + 3ab + 3b² + 6b
- a(a+3b+2) + b(a+3b+2) = a² + 3ab + 2a + ab + 3b² + 2b
Step 3: Combine Like Terms
Now, we combine the like terms:
- (a² + a² ) + (ab + 3ab + ab) + (2a + 2a) + (3b² + 3b²) + (6b + 2b) = 2a² + 5ab + 4a + 6b² + 8b
Step 4: Subtract the Second Expression
Finally, we subtract the expanded second expression from the expanded first expression:
(2a² + 5ab + 4a + 6b² + 8b) - (a² + 3ab + 2a + ab + 3b² + 2b)
Step 5: Simplify
Combining like terms again, we arrive at the simplified expression:
- (2a² - a²) + (5ab - 3ab - ab) + (4a - 2a) + (6b² - 3b²) + (8b - 2b) = a² + ab + 2a + 3b² + 6b
Therefore, the simplified form of the expression (a+3b)(a+b+2)-(a+b)(a+3b+2) is a² + ab + 2a + 3b² + 6b.