Problem 51 - Introductory Algebra for College Students

Question

Simplify each algebraic expression. $$-8 a+(-15 a)$$

Step-by-Step Solution

Answer

The simplified form of this algebraic expression is \( -23a \)

Step 1: Identify Like Terms

In the expression \( -8a + (-15a) \), you can see two 'like terms', \( -8a \) and \( -15a \). Like terms are terms with the same variable(s) and exponent(s). In this case, both terms are multiples of 'a'.

Step 2: Combine Like Terms

Like terms can be combined using addition or subtraction - in this case, since both terms are negative you add the coefficients together. So divide the problem into two parts: 1. Coefficients: -8 and -15, 2. Common variable: a. Adding these coefficients together gives you \( -8 + -15 = -23 \).

Step 3: Rewrite the Expression

Finally, rewrite the combined terms as the simplified expression. The combined term is \( -23a \), which is the simplified version of the original expression.