To demonstrate why the product [tex]\((-6)(-3)\)[/tex] is positive using the distributive property, we start with the equation provided:
[tex]\[(-6)(-3) + (-6)(3) = (-6)[(-3) + 3]\][/tex]
Let’s go through this step-by-step:
1. Distribute (-6) to the sum inside the brackets:
[tex]\[(-6)(-3) + (-6)(3) = (-6)(-3 + 3)\][/tex]
2. Simplify the expression inside the brackets:
[tex]\[(-3) + 3 = 0\][/tex]
So, the equation becomes:
[tex]\[(-6)(-3) + (-6)(3) = (-6) \times 0\][/tex]
3. Multiply (-6) by 0:
[tex]\[
(-6) \times 0 = 0
\][/tex]
Since any number multiplied by zero is zero, we have:
[tex]\[
(-6)(-3) + (-6)(3) = 0
\][/tex]
4. Now isolate [tex]\((-6)(-3)\)[/tex]:
Let's denote [tex]\((-6)(-3)\)[/tex] as [tex]\(x\)[/tex]. The original equation can be rewritten as:
[tex]\[
x + (-6)(3) = 0
\][/tex]
5. To solve for [tex]\(x\)[/tex], add [tex]\(6 \times 3\)[/tex] to both sides:
[tex]\[
x = 6 \times 3
\][/tex]
6. Calculate [tex]\(6 \times 3\)[/tex]:
[tex]\[
6 \times 3 = 18
\][/tex]
So, we find:
[tex]\[
x = 18
\][/tex]
Thus, [tex]\((-6)(-3) = 18\)[/tex]. This shows that [tex]\((-6)(-3)\)[/tex] is positive because the product of two negative numbers is positive.
