#separator:tab #html:false #tags column:4 Commutative property of addition a + b = b + a math-algebra-rules Commutative property of multiplication ab = ba math-algebra-rules Associative property of addition (a + b) + c = a + (b + c) math-algebra-rules Associative property of multiplication (ab)c = a(bc) math-algebra-rules Distributive property a(b + c) = ab + ac math-algebra-rules Additive identity a + 0 = a math-algebra-rules Multiplicative identity a × 1 = a math-algebra-rules Additive inverse a + (−a) = 0 math-algebra-rules Multiplicative inverse a × (1/a) = 1, for a not zero math-algebra-rules Zero property of multiplication a × 0 = 0 math-algebra-rules Reflexive property a = a math-algebra-rules Symmetric property If a = b, then b = a math-algebra-rules Transitive property If a = b and b = c, then a = c math-algebra-rules Addition property of equality If a = b, then a + c = b + c math-algebra-rules Multiplication property of equality If a = b, then ac = bc math-algebra-rules Substitution property If a = b, then b can replace a in any expression math-algebra-rules Rule for multiplying two negatives The product is positive math-algebra-rules Rule for multiplying a negative and a positive The product is negative math-algebra-rules Rule for dividing two negatives The quotient is positive math-algebra-rules Subtracting a negative a − (−b) = a + b math-algebra-rules Solve x + 7 = 12 x = 5 math-algebra-rules Solve 3x = 21 x = 7 math-algebra-rules Solve 2x − 5 = 9 x = 7 math-algebra-rules Solve x/4 = 6 x = 24 math-algebra-rules Solve 5x + 3 = 2x + 15 x = 4 math-algebra-rules Rule for inequalities Multiplying or dividing by a negative number flips the inequality sign math-algebra-rules Solve −2x > 6 x < −3 math-algebra-rules Solve |x| = 5 x = 5 or x = −5 math-algebra-rules Solve |x| < 3 −3 < x < 3 math-algebra-rules Solve |x| > 3 x < −3 or x > 3 math-algebra-rules FOIL First, Outer, Inner, Last: multiplying two binomials math-algebra-rules Expand (x + 3)(x + 2) x² + 5x + 6 math-algebra-rules Expand (x + 4)² x² + 8x + 16 math-algebra-rules Expand (x − 5)² x² − 10x + 25 math-algebra-rules Expand (x + 3)(x − 3) x² − 9 math-algebra-rules Factor x² + 7x + 12 (x + 3)(x + 4) math-algebra-rules Factor x² − 9 (x − 3)(x + 3) math-algebra-rules Factor x² − 5x + 6 (x − 2)(x − 3) math-algebra-rules Factor x² + 2x + 1 (x + 1)² math-algebra-rules Factor 2x² + 6x 2x(x + 3) math-algebra-rules Sum of cubes a³ + b³ = (a + b)(a² − ab + b²) math-algebra-rules Difference of cubes a³ − b³ = (a − b)(a² + ab + b²) math-algebra-rules Binomial cube (a + b)³ = a³ + 3a²b + 3ab² + b³ math-algebra-rules Solve x² = 49 x = 7 or x = −7 math-algebra-rules Solve x² − 5x + 6 = 0 x = 2 or x = 3 math-algebra-rules Midpoint of two numbers Their average: (a + b)/2 math-algebra-rules Cross-multiplication If a/b = c/d, then ad = bc math-algebra-rules Adding fractions with unlike denominators Use a common denominator first math-algebra-rules Slope between two points (y₂ − y₁)/(x₂ − x₁) math-algebra-rules Perpendicular to slope 2 Slope −1/2 math-algebra-rules Distance, rate, time d = r × t math-algebra-rules Percent change (new − old) / old × 100% math-algebra-rules Simple interest I = P r t math-algebra-rules Average (mean) formula Sum of values divided by number of values math-algebra-rules Order of solving with variables on both sides Collect variable terms on one side, constants on the other, then divide math-algebra-rules Check a solution Substitute it back into the original equation math-algebra-rules