Problem 90 - Algebra and Trigonometry

Question

Simplify each algebraic expression. $$4(2 y-6)+3(5 y+10)$$

Step-by-Step Solution

Answer

The simplified expression is \(23y + 6\)

Step 1: Distribute the numbers over each term inside the parentheses

For the first term, multiply 4 by each term in the parentheses (2y & -6). This yields: \(8y - 24\). Repeat the process for the second term, multiplying 3 by each of the terms inside the parentheses (5y & 10) to get \(15y + 30\).

Step 2: Combine all terms

Next, combine the results of the first and second term. So, write down \(8y - 24 + 15y + 30\).

Step 3: Combine like terms

The like terms in expression are 8y and 15y, then -24 and 30. To add 8y and 15y, obtain \(23y\). Furthermore, adding -24 and 30 equals to 6. Hence the simplified expression is \(23y + 6\)