Revision sheet · Mathematics

Algebraic identities

Square of a sum: $(a + b)^{2} = a^{2} + 2 ab + b^{2}$
Square of a difference: $(a - b)^{2} = a^{2} - 2 ab + b^{2}$
Square of a sum of three terms: $(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 ab + 2 b c + 2 c a$
Difference of two squares: $(a + b) (a - b) = a^{2} - b^{2}$
Product of (x + a) and (x + b): $(x + a) (x + b) = x^{2} + (a + b) x + ab$
Product of (ax + b) and (cx + d): $(a x + b) (c x + d) = a c x^{2} + (a d + b c) x + b d$
Cube of a sum: $(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}$
Cube of a difference: $(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}$
Difference of two cubes: $a^{3} - b^{3} = (a - b) (a^{2} + ab + b^{2})$
Sum of two cubes: $a^{3} + b^{3} = (a + b) (a^{2} - ab + b^{2})$
a³ + b³ + c³ − 3abc: $a^{3} + b^{3} + c^{3} - 3 ab c = (a + b + c) (a^{2} + b^{2} + c^{2} - ab - b c - c a)$