Question

Given the expression below, correctly identify the parts.
(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 \( 5x - 35 \)