Algebra 1 Cheat Sheet
An expression of the form:
axxn+an−1xn−1+· · · +a2x2+a1x+a0
Where ai∈R;i= 0,1,2, . . . , n;n∈N.
Polynomial
Linear (degree 1) ax +b
Quadratic (degree 2) ax2+bx +c
Cubic (degree 3) ax3+bx2+cx +d
Types Of Polynomials
Difference Of Two Squares a2
−b2= (a+b)(a−b)
Difference Of Two Cubes a3
−b3= (a−b)(a2+ab+b2)
Sum Of Two Cubes a3+b3= (a+b)(a2
−ab+b2)
Factoring
(x3+x2−2x)÷(x−1)
Solution:
x2+ 2x
x−1x3+x2−2x
−x3+x2
2x2−2x
−2x2+ 2x
0
Polynomial Long Division
a(b
c) = ab
c
(a
b)
c=a
bc
a
(b
c)=ac
b
(a
b)
(c
d)=ad
bc
a
b+c
d=ad +bc
bd
a+b
c=a
c+b
c
ab +ac
a=b+c, a 6= 0
Algebraic Fractions
The binomial coefficient represents the number of
ways you can choose robjects from a group of nob-
jects.
n
r=n!
r!(n−r)! n
r=n
n−r
n
r=n(n−1)(n−2) . . . (n−(k−1))
k(k−1)(k−2) . . . 1
Binomial Coefficient
For any positive integer n,
(a+b)n=
n
X
m=0 n
man−mbn
=n
0an+n
1an−1b1+· · · +n
nbn
Binomial Theorem
In an identity, all coefficients of like powers are
equal.
An identity must be true for all values of the inde-
pendent variables
Example: 3x+ 7 = ax +bimplies a= 3 and
b= 7.
Algebraic Identities
What you do to one side of an equation, you
must do to the other.
In terms of xWrite with xas the inde-
pendent variable
The subject of Make it on it’s own on one
side of the equation
As a function of same as ’in terms of’
Manipulating Formulae
Linear equations can be solved by making x with sub-
ject of the equation.
Example: Solve 4x+ 2 = 14
4x+ 2 = 14
=⇒4x= 14 −2 = 12
=⇒x=12
4= 3
Solving Linear Equations
1. Reduce the three equations to two by eliminating
one of the unknowns.
2. Choose an unknown to isolate.
3. Eliminate this unknown from all three equations,
taking them two at a time.
4. Solve these two equations.
5. Use the solutions as values in the original equations
6. Check your solution!
Systems of Equations With Three Variables
1
