Distributive property

Question

Simplify (x + 1)(x – 3)

Answer 1

Almost always, the Distributive Property is written as:  a(b+c) = ab + ac.

So, in this problem:
    (x+1)(x-3)  =  (x+1)(x) + (x+1)(-3)

Now, you may apply the Commutative Property (ab = ba) then apply the Distributive Property again twice more:

    (x+1)(x) = (x)(x+1)
    (x)(x+1) = x^2 + x and

    (x+1)(-3) = (-3)(x+1)
<    (-3)(x+1) = -3x+ -3

That gives:
    (x+1)(x-3) = x^2 + x - 3x - 3       [This is F-I-OL, not F-O-I-L]
    (x+1)(x-3) = x^2 - 3x + x - 3       [Commute; now is F-O-I-L]
<    (x+1)(x-3) = x^2 -2x - 3                       [combine like terms]

Answer 2

Most people use FOIL..

First, Outside, Inside, Last

 

That's fine but I find it simpler to

just multiply the first term in 1st

parenthesis through, then the next.

 

(x+1)(x-3)

= x(x) + x(-3) +1(x) + 1(-3)

= x² - 3x + x - 3

= x² - 2x - 3