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

Question

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?

@LordSharktheUnknown Ah, that would make a difference. Thank you! — General Nuisance, Sep 01 '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 01 '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 01 '17 at 18:25
@DonaldSplutterwit Right! One term. So the distributive property applies only to terms within a group? — General Nuisance, Sep 01 '17 at 18:27
That's right ... littleO's example illustrates several terms ... yours only has one. — Donald Splutterwit, Sep 01 '17 at 18:29
Thank you all! I would be happy to accept an answer that explains that I was mis-using the distributive property. — General Nuisance, Sep 01 '17 at 18:31

score 3 · Accepted Answer · answered Sep 01 '17 at 19:10

3

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 $$ \underbrace{a(bc) = (ab)(ac)}_{\text{usually false}}. $$

answered Sep 01 '17 at 19:10

littleO

51,938

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

1 Answers1