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

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

Expanding 4(a+1):
 Multiply 4 by each term inside the parentheses:
 4 * a = 4a
 4 * 1 = 4

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.