Suppose you used the distributive property to get the expression 12x + 3y - 9. With what expression could you have started?

Answer 1

To find an expression that could lead to \( 12x + 3y - 9 \) using the distributive property, we can factor out a common term from the expression.

Observe the coefficients of \( x \), \( y \), and the constant term:

• The coefficients are \( 12 \) for \( x \), \( 3 \) for \( y \), and \( -9 \) is a constant.

We notice that \( 3 \) is a common factor of \( 12 \), \( 3 \), and \( -9 \). So we can factor \( 3 \) out of each term:

\[ 12x + 3y - 9 = 3(4x + y - 3) \]

Thus, we could have started with the expression \( 3(4x + y - 3) \).

This is the expression from which you could apply the distributive property to arrive at \( 12x + 3y - 9 \).