Algebra Rules
Exponents, factoring, and the identities you rearrange most often.
Exponent laws
| Rule | Formula | Example |
|---|
| am⋅an=am+n | 23⋅22=25=32 |
| am/an=am−n | x5/x2=x3 |
| (am)n=amn | (x2)3=x6 |
| (ab)n=anbn | (2x)3=8x3 |
| a−n=1/an | 2−3=1/8 |
| a0=1 (a=0) | |
| a1/n=na | |
Factoring & expansion
| Rule | Formula | Example |
|---|
| a(b+c)=ab+ac | 3(x+2)=3x+6 |
| (a+b)2=a2+2ab+b2 | (x+3)2=x2+6x+9 |
| (a−b)2=a2−2ab+b2 | (x−2)2=x2−4x+4 |
| a2−b2=(a+b)(a−b) | x2−9=(x+3)(x−3) |
| ab+ac=a(b+c) | 6x2+4x=2x(3x+2) |
Quadratics
For $ax^2 + bx + c = 0$ with $a \ne 0$.
| Rule | Formula | Example |
|---|
| x=2a−b±b2−4ac | x2−5x+6=0⇒x=2,3 |
| Δ=b2−4ac | Δ>0: two real roots; Δ=0: one; Δ<0: none real |
| x1+x2=−b/a, x1x2=c/a | For x2−5x+6: sum =5, product =6 |