Question

Explain how you know whether to add or subtract when you use the distributive property to multiply

Answer 1

Distributive property of multiplication has two expressions:

1. $a\cdot (b+c)=a\cdot b+a\cdot c$

2. $a\cdot (b-c)=a\cdot b-a\cdot c$

If you use these formulas from the left side to the right side, you should see for the sign in the brackets: "+" - use addition, "-" - use subtraction. If you use these formulas from the right side to the left side, you should also take into account sign between $a\cdot b$ and $a\cdot c$: for "+" - use addition in brackets and for "-" - use subtraction in brackets.

Answer 2

The correct answer is:

We treat the addition or subtraction signs inside the parentheses as positive and negative signs and follow our integer rules.

Explanation:

Take for example -3(x+y). The distributive property tells us to take -3*x + -3*y; we have a positive multiplied by a negative, which is a negative, and another positive multiplied by a negative, which is again a negative. This gives us -3x+-3y, or -3x-3y.

If we consider the sign of the value outside the parentheses as well as the signs of those inside, we can be sure to use the write operation sign.