We saw in the prealgebra section
that we can combine like terms, like 2n + 3n = 5n.
We also used the distributive law to expand numbers; here we distribute the 7:
7*13 = 7(10 + 3) = 7*10 + 7*3
= 70 + 21 = 91.
Also this works with variables;
we state the law usually as a(b + c) = ab + ac.
In a typical algebra problem
you're asked to expand something like 5(x + 7).
5(x + 7) = 5(x) + 5(7) =
5x + 35. This problem was. . . no problem!
- When faced with an expression
like 4x + 5(3x - 12), what do we do first?
- Let's see: PEMDAS says work
in parentheses first, but 3x and 12 are unlike.
- Hmm, let's try the distributive law again, but just with the multiplied
- 4x + 5(3x -
- = 4x + 5(3x) -
- = 4x + 15x - 60
- = 19x - 60 . That's
our answer, simplified.
about (4x + 5)(3x - 12) ? Is this the same as 4x + 5(3x - 12) ?
No, the parentheses change
it. Here we can use the distributive law twice:
(4x + 5)(3x - 12)
= (4x + 5)(3x) -
(4x + 5)(12)
= 12x^2 + 15x - 48x -
60 (remember to change the sign
on that last term)
12x^2 - 33x - 60 . That worked, but it was long.
Is this the only way? No.
The best way? No. Use the "FOIL system":
First, Outside, Inside,