(a+3)(a+1)-4(a+1)

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression (a+3)(a+1)-4(a+1)

This article will guide you through simplifying the expression (a+3)(a+1)-4(a+1). We'll break down the steps and use the distributive property to reach a simplified form.

Understanding the Expression

The expression consists of two terms:

• (a+3)(a+1): This is a product of two binomials, which can be expanded using the distributive property (also known as FOIL).
• -4(a+1): This is a monomial multiplied by a binomial, which can also be simplified using the distributive property.

Simplifying using the Distributive Property

1. Expanding (a+3)(a+1):

   • Multiply each term in the first binomial by each term in the second binomial:
   • a * a = a²
   • a * 1 = a
   • 3 * a = 3a
   • 3 * 1 = 3
   • Combine the terms: a² + a + 3a + 3
   • Simplify by combining like terms: a² + 4a + 3

2. Expanding -4(a+1):

   • Multiply -4 by each term inside the parentheses:
   • -4 * a = -4a
   • -4 * 1 = -4

3. Combining the results:

   • Our expression now looks like this: a² + 4a + 3 - 4a - 4
   • Combine like terms: a² + (4a - 4a) + (3 - 4)
   • Simplify: a² - 1

Final Result

The simplified form of the expression (a+3)(a+1)-4(a+1) is a² - 1.