Question

Which expression is equivalent to 8(x + 4) + 12x after using the distributive property?

1) 8x + 32 + 12x
2) 8x + 4 + 12x
3) 8x + 4 + 12
4) 8x + 32 + 12

Answer 1

The simplified form of the expression 8(x + 4) + 12x, after using the distributive property and combining like terms, is equivalent to 20x + 32, which corresponds to option 1) 8x + 32 + 12x.

Step-by-step explanation:

The expression 8(x + 4) + 12x is to be simplified using the distributive property. The distributive property allows us to multiply the number outside the parentheses by each term inside the parentheses. Here's how it works step by step:

• First, distribute the 8 to both terms inside the parentheses: 8 * x + 8 * 4.
• Next, simplify the multiplication: 8x + 32.
• Finally, add the 12x that is outside the parentheses to the simplified expression: 8x + 32 + 12x.
• Combine like terms by adding the coefficients of x: 20x + 32.

Therefore, after using the distributive property and combining like terms, the expression is equivalent to 20x + 32, which means option 1) 8x + 32 + 12x is the correct equivalent expression.