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In algebra, an equivalent expression is an expression that has the same value as another expression, even though it may look different. This means that when you simplify or rearrange the expressions, their value stays the same.

For example, in the given exercise, we started with the expression:

• 3(a + 5)

By using the distributive law, we simplified this to:

• 3a + 15

Both expressions are equivalent because they represent the same value for any given value of a.

Understanding equivalent expressions is crucial because it helps in simplifying complex expressions and solving equations.

When you encounter a problem requiring equivalent expressions, think of it as redefining the same information in a different form.

Multiplying binomials is a crucial skill in algebra. In the exercise, we deal with the binomial expression (a + 5).

When multiplying a binomial by a single term, the distributive law tells us to multiply each term inside the parentheses by the term outside.

With the expression 3(a + 5), we break it down as follows:

• First, multiply 3 by a, which results in 3a.
• Then, multiply 3 by 5, which gives us 15.

We then combine these products to form the simplified equivalent expression:

• 3a + 15

By following these straightforward steps, you can multiply any binomial by a monomial.

Mastering this technique will allow you to handle more complex algebraic expressions with confidence.

Algebraic expressions are mathematical phrases that can contain numbers, variables, and operations. In general, algebraic expressions help us model real-world situations and solve problems.

An algebraic expression may contain:

• Constants, like the number 5 in the expression.
• Variables, such as 'a' in the expression.
• Operations, including addition (+) and multiplication (*).

In our exercise, the algebraic expression is 3(a + 5). We used algebraic manipulation to apply the distributive law and simplify the expression:

• 3(a + 5)

This becomes:

• 3a + 15

Understanding algebraic expressions and how to manipulate them is fundamental in algebra. This forms the basis for more advanced topics, such as solving equations and inequalities.