- High schoolπ€Algebra0οΈβ£
Zero product equation: A Γ B = 0 in 2 seconds
If a product equals 0, at least one factor is 0. The rule that cracks every factored equation.
- High schoolπ€Algebraβ
1 + 2 + 3 + ... + n = n(n+1)/2: Gauss's formula
Young Gauss found it at age 8 by folding the series on itself. One of the most elegant results in math.
- Middle schoolπ€Algebraπ§©
System of 2 equations, 2 unknowns: substitution that always works
Isolate, substitute, solve. The 3-step substitution method, with no sign-error risk.
- Middle schoolπ€AlgebraΒ²
Rules for computing with powers: the printable sheet
Multiply, divide, raise to a power⦠5 rules that cover every case in middle and high school.
- High schoolπ€Algebraβ‘
Spot a notable identity in 2 seconds flat
$(a+b)^2$, $(a-b)^2$, $a^2-b^2$: three patterns to recognize with your eyes closed. The 3 reflexes that speed up the whole chapter.
- High schoolπ€AlgebraβοΈ
n-th roots of unity: vertices of a regular polygon
The n solutions of z^n = 1 are e^(2ikΟ/n). They form a regular polygon on the unit circle.
- College prepπ€Algebraπ’
Matrices: addition, multiplication, transpose
The 3 basic matrix operations. Dimension rules, non-commutativity, transpose.
- Middle schoolπ€AlgebraβοΈ
Linear inequality: the sign-flip trap
Solve like an equation, but if you multiply or divide by a negative, FLIP the inequality.
- Middle schoolπ€Algebra=
Linear equation: the 4-step method
Expand, gather x on one side and the rest on the other, divide. A reliable routine.
- High schoolπ€Algebraπ¨
Factor a trinomial when you know its roots
If $x_1$ and $x_2$ solve $ax^2 + bx + c = 0$, then $ax^2 + bx + c = a(x - x_1)(x - x_2)$. Free factorization.
- Middle schoolπ€Algebraπ§
Expand and simplify: the routine k(a+b) = ka+kb
Distribute, then collect like terms. The basic algebra move in middle school.
- Middle schoolπ€AlgebraβοΈ
Expanding (a+b)(c+d): the 'each with each' method that forgets nothing
FOIL / double distribution in 4 visual steps. The safest way to avoid missing terms.