Problem 90 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

The simplified version of the expression \(4(2 y-6) + 3(5 y+10)\) is \(23y + 6\)

Step 1: Apply the distributive property

Begin by applying the distributive property. Multiply each term inside the parentheses by the factor outside the parentheses. For the first term, this gives \(4 * 2y = 8y\) and \(4 * -6 = -24\). For the second term, we get \(3 * 5y = 15y\) and \(3 * 10 = 30\). So the expression now becomes \(8y - 24 + 15y + 30\)

Step 2: Combine like terms

Next, combine the similar terms i.e. \(8y + 15y = 23y\) and \(-24 + 30 = 6\). The simplified expression thus becomes \(23y + 6\)