(x%2B2)-expand-and-simplify.jpeg "(x+3)(x+2) Expand And Simplify")
Expanding and Simplifying (x+3)(x+2)
In algebra, multiplying two binomials is a fundamental operation. In this article, we will explore how to expand and simplify the product of two binomials, specifically, (x+3)(x+2).
The Distributive Property
To expand the product of two binomials, we can use the distributive property of multiplication over addition, which states that:
a(b + c) = ab + ac
This property allows us to multiply each term in one binomial by each term in the other binomial.
Expanding (x+3)(x+2)
Using the distributive property, we can expand (x+3)(x+2) as follows:
(x+3)(x+2) = x(x+2) + 3(x+2)
= x^2 + 2x + 3x + 6
Combining Like Terms
Now, we can combine like terms to simplify the expression:
x^2 + 2x + 3x + 6 = x^2 + 5x + 6
Simplified Form
The final simplified form of (x+3)(x+2) is:
x^2 + 5x + 6
In conclusion, we have successfully expanded and simplified the product of two binomials, (x+3)(x+2), using the distributive property and combining like terms. This exercise has demonstrated the importance of following the order of operations and applying algebraic properties to simplify complex expressions.
