(a+3b)(a+b+2)-(a+b)(a+3b+2)

Jasonbradley

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Jun 16, 2024

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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.