Given the expression below, correctly identify the parts.

Question

(Which parts are the Constant(s)? Variable(s)? Coefficient(s)? Distributive Property?)

3x + 5(x - 7) - 8y

Answer 1

Let's break down the expression \( 3x + 5(x - 7) - 8y \) into its components:

1. Constants: These are numbers that do not change and are not multiplied by any variables. In the expression, the constants are:

   • 5
   • -7 (inside the parentheses with \( x \))
   • -8 (the coefficient of \( y \))

2. Variables: These are symbols that represent unspecified numbers. In the expression, the variables are:

   • \( x \)
   • \( y \)

3. Coefficients: These are the numerical factors that multiply the variables. In the expression, the coefficients are:

   • 3 (for \( x \))
   • 5 (as the coefficient of the term \( (x - 7) \), which means \( 5 \times x \) and \( 5 \times -7 \))
   • -8 (as the coefficient of \( y \))

4. Distributive Property: The distributive property refers to distributing a coefficient across a parenthetical expression. In this expression, the distributive property is applied to the \( 5(x - 7) \) term. This can be rewritten as:

   • \( 5 \cdot x - 5 \cdot 7 = 5x - 35 \)

So, putting it all together, we identify the parts of the expression \( 3x + 5(x - 7) - 8y \) as follows:

• Constants: 5, -7, -8
• Variables: \( x \), \( y \)
• Coefficients: 3, 5, -8
• Distributive Property: Used in \( 5(x - 7) \) which expands to \( 5x - 35 \)