- High school🔤Algebra⚡
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 school🔤Algebra🔨
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 school🔤Algebra🔗
Distributive property: expand without ever getting it wrong
$k(a+b) = ka + kb$: the rule, one key move, two traps to avoid. The bedrock of algebra.
- College prep🔤Algebra🔺
$(a+b)^n$: binomial theorem and Pascal's triangle
Expand $(a+b)^n$ without multiplying $n$ times: coefficients come from Pascal's triangle, powers follow a simple rule.
- College prep🔤Algebra⚡
Diagonalize a 2×2 matrix in 60 seconds
Trace, determinant, discriminant. Three calculations and boom, your eigenvalues. Then eigenvectors in three lines each.
