Special products
(a - b) (a + b) = a^2 - b^2
(a - b)^2 = a^2 - 2ab + b^2
(a + b)^2 = a^2 + 2ab + b^2
FOIL
First terms, outside terms, inside terms, last terms
Common Factors
What does it mean when a polynomial is whole squared
ex. (a + 3b)^2
It means the polynomial is multiplied by itself.
ex. (a + 3b) (a + 3b)
How do you use GCF
You write GCF as the first factor outside the bracket and divide each term in the brackets by the GCF
How to factor a trinomial in the form x^2 + bx + c
Utilise PSN, find two numbers that add to B and multiply to C
Ex. x^2 - 10x + 16
Dissect the second term into the two numbers
X^2 - 8x - 2x + 16
Group the first two and last two terms together
X(x - 8) - 2(x -8)
Utilise Binomial as a common factor
(x - 8) (x - 2)
What is Binomial as a common factor
There are two separate terms with a common binomial.
Opposite of Expanding
Factoring
Factoring by grouping
This is done in order to have a binomial as a common factor. You must group terms that have a common factor, and the variable in the terms must be equally split
ex. ac + bc + ad + bd
There is two C variables and two D variables, therefore you group those two together
= a(c + d) + b (c + d)
= (c + d) (a + c)
How to factor ax^2 + bx + c
Find two numbers that multiply to A multiplied by C and add to B
ex. 3y^2 + y - 4 P S N
=3y^2 -3y + 4y - 4 -12 1 4, -3
= 3y (y-1) + 4(y-1)
= (y - 1) (3y + 4y)
Factoring difference of squares
For a^2 - b^2 you would do
ex. x^2 - 49
= x^2 - 7^2
= (x + 7) (x - 7)
3 rules for factoring using difference of squares
Only two terms
Both terms must be perfect squares
The sign in between both terms must be negative
