(a%2Bc)-simplify.jpeg "(a+b)(a+c) Simplify")
Simplifying (a+b)(a+c)
In algebra, simplifying expressions is an essential skill to master. One of the most common expressions to simplify is the product of two binomials, such as (a+b)(a+c). In this article, we will explore how to simplify this expression step by step.
Step 1: Multiply the Two Binomials
To simplify (a+b)(a+c), we need to multiply the two binomials using the distributive property of multiplication over addition. The distributive property states that:
a(b+c) = ab + ac
Using this property, we can expand the product of the two binomials as follows:
(a+b)(a+c) = a(a+c) + b(a+c)
Step 2: Expand the Expression
Now, we need to expand the expression by multiplying each term in the first binomial by each term in the second binomial:
a(a+c) = a^2 + ac
b(a+c) = ba + bc
So, the expanded expression becomes:
(a+b)(a+c) = a^2 + ac + ba + bc
Step 3: Simplify the Expression
Finally, we can simplify the expression by combining like terms:
a^2 + ac + ba + bc = a^2 + ac + ab + bc
And that's the simplified expression!
Simplified Expression:
(a+b)(a+c) = a^2 + ac + ab + bc
By following these three steps, we have successfully simplified the expression (a+b)(a+c). This skill is essential in algebra and will be used extensively in more advanced mathematical topics.
