a(b+c) = ab+ac
(a+b)(c+d) = ac+ad+bc+bd
(a+b)² = (a+b)(a+b)
HCF · Grouping · Split-the-middle
Two numbers: product=constant, sum=middle
Multiply bottoms, cross-multiply tops
Cross the equals → flip the sign
Inequalities: change-change for negatives
Different signs add, same signs subtract
Multiply to match, then back-substitute
A×B=0 → A=0 or B=0
x = (-b ± √(b²-4ac)) / 2a
a^p·a^q = a^(p+q)
a^p÷a^q = a^(p-q)
(a^p)^q = a^(pq) · √x = x^(1/2)
solve: same base → equate powers