# Distributive Property: How come I get a different answer by distributing than by solving inside the parenthesis first?

Consider the closed phrase:

$$-(2\cdot2\cdot2\cdot2)$$

If I distribute $-1$, I get:

$$-1(2\cdot2\cdot2\cdot2)= -2\cdot-2\cdot-2\cdot-2= 16$$

If I solve in the parenthesis first:

$$-(2\cdot2\cdot2\cdot2)=-(16)=-16$$

Aren't both of these valid ways to solve this phrase?

• multiplication does not distribute over multiplication – Angina Seng Sep 1 '17 at 18:24
• @LordSharktheUnknown Ah, that would make a difference. Thank you! – General Nuisance Sep 1 '17 at 18:24
• The distributive property would tell you that $-1 \times(2 + 2 + 2 + 2) = -1 \times 2 + -1 \times 2 + -1 \times 2 + -1 \times 2$. – littleO Sep 1 '17 at 18:25
• You would be correct to say that the $-1$ multiplies everything in the bracket ... but you would need to understand that $2 \times 2 \times 2 \times 2$ only counts as one thing. – Donald Splutterwit Sep 1 '17 at 18:25
• @DonaldSplutterwit Right! One term. So the distributive property applies only to terms within a group? – General Nuisance Sep 1 '17 at 18:27

The distributive rule says that if $a,b,$ and $c$ are numbers then $$a(b + c) = ab + ac.$$ However, there is no rule which says that $$\underbrace{a(bc) = (ab)(ac)}_{\text{usually false}}.$$