Algebra

Sub numbers in (brackets), BOMDAS. Combine only like terms; x means 1x.

a(b+c)=ab+ac. (a+b)(c+d): split, distribute, collect. (a+b)²=(a+b)(a+b).

HCF: lift the common piece. Grouping: pair up four terms. Trinomial: two numbers multiply to the constant, add to the middle — split and group. Always multiply back to check.

Multiply the bottoms; cross-multiply the tops with brackets; a subtraction flips both signs.

Divide-multiply-subtract-bring down. To rearrange, do the same to both sides; factorise if the letter is on both sides.

Move terms across the equals, flipping signs. Inequalities are the same — but flip the direction when you multiply/divide by a negative.

Eliminate a letter (different signs add, same signs subtract); multiply first to make coefficients match, then back-substitute.

If A×B=0 then A or B = 0 — factorise and set each bracket to zero. Spot difference of squares. If it won't factorise, use the -b formula.

Multiply → add powers: a^p·a^q = a^p+q. Divide → subtract: a^p/a^q = a^p−q. Power of a power → multiply: (a^p)^q = a^pq.

a^1/p = the p-th root of a. In particular √x = x^1/2.

Write both sides as powers of the same base, then the powers must be equal. Rewrite awkward bases first (9 = 3², 27 = 3³).