First, Outer, Inner, Last. Every binomial multiplication follows this exact order. Never miss a term again.
F
First — multiply the first terms of each binomial
O
Outer — multiply the outermost terms
I
Inner — multiply the innermost terms
L
Last — multiply the last terms of each binomial
🔢 Algebra
Please Excuse My Dear Aunt Sally
Order of Operations
PEMDAS — never solve in the wrong order
Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. Always in this sequence.
P
Parentheses first
E
Exponents
M
Multiplication (left to right)
D
Division (left to right)
A
Addition (left to right)
S
Subtraction (left to right)
🔢 Algebra
"Difference of Squares"
a² − b² = (a+b)(a−b)
Factor any difference of two perfect squares instantly
Spot two perfect squares being subtracted? Factor immediately: a² − b² = (a+b)(a−b). This pattern is on every algebra exam.
🔢 Algebra
Slope = Rise / Run
Slope Formula
Never confuse rise and run again
Rise is the vertical change (y₂ − y₁). Run is the horizontal change (x₂ − x₁). Rise over Run = slope. Think: you rise UP before you run ACROSS.
🔢 Algebra
"Slide and Divide"
Factoring ax² + bx + c
Factor trinomials with a leading coefficient fast
Multiply a and c together (slide). Factor that product with b. Divide by a and simplify. Works every time for hard trinomials.
Quadratic Formula
Quadratic formula: x = (-b ± √(b²-4ac)) / 2a — 'Pop goes the weasel' rhythm helps
Quadratic Formula
Solve any quadratic ax²+bx+c=0 — memorize this cold
Sing it to 'Pop Goes the Weasel': 'x equals negative b, plus or minus square root, b squared minus 4ac, all over 2a.' The discriminant (b²-4ac): positive = 2 real roots, zero = 1 real root, negative = no real roots.
Zero Product Property
Zero product property: if (x-3)(x+2)=0, then x=3 or x=-2
Zero Product Property
If a product equals zero, at least one factor must be zero
Set each factor equal to zero and solve. (x-5)(x+4)=0 → x=5 or x=-4. This is why factoring works to solve quadratics. Factor the quadratic, set each factor to zero, solve for x.
Solving Systems of Equations
Systems of equations: substitution (plug in) or elimination (add/subtract rows)
Solving Systems of Equations
Two methods for finding where two equations intersect
Substitution: isolate one variable, plug into other equation. Best when one equation is already solved for a variable. Elimination: multiply equations to make coefficients match, add or subtract to eliminate one variable. Best when coefficients are easy to match.
Four rules that cover almost every exponent problem
Multiply same base: ADD exponents. Divide same base: SUBTRACT exponents. Power to a power: MULTIPLY exponents. Anything to the zero power = 1. Negative exponent: x⁻ⁿ = 1/xⁿ (flip to denominator). Fractional exponent: x^(1/n) = ⁿ√x.
Multiply
xᵃ · xᵇ = xᵃ⁺ᵇ — add exponents
Divide
xᵃ ÷ xᵇ = xᵃ⁻ᵇ — subtract exponents
Power
(xᵃ)ᵇ = xᵃᵇ — multiply exponents
Zero
x⁰ = 1 always
Absolute Value
Absolute value: |x| = distance from zero. Always positive. |x| = a means x = a or x = -a
Absolute Value
Distance from zero — always non-negative
|-5| = 5. |3| = 3. When solving |x-2| = 5: set up two equations, x-2 = 5 (x=7) AND x-2 = -5 (x=-3). For inequalities: |x| < a means -a < x < a (AND). |x| > a means x > a OR x < -a.
Function Notation
Function notation: f(x) means 'f of x' — plug x in wherever you see the variable
Function Notation
Reading and evaluating function notation
f(x) = 2x + 3. Find f(4): replace x with 4 → f(4) = 2(4)+3 = 11. f(x+1): replace x with (x+1) → 2(x+1)+3 = 2x+5. Composition: f(g(x)) means find g(x) first, then plug that into f.
Inequality Rules
Inequalities: flip the sign when multiplying or dividing by a NEGATIVE number
Inequality Rules
The one rule students always forget — flip when dividing by negative
-2x > 6 → divide both sides by -2 → x < -3 (sign flips). On a number line: < and > use open circles. ≤ and ≥ use closed circles. Interval notation: x > 3 is (3, ∞). x ≤ 5 is (-∞, 5].