Special Factoring Patterns

Quadratics and polynomialsSpecial Factoring PatternsQuadratic Equations and Parabolas Polynomial Theorems

Squares

Difference of squares

a^{2} - b^{2} = (a - b) (a + b)

Square of a sum

(a + b)^{2} = a^{2} + 2 a b + b^{2}

Square of a difference

(a - b)^{2} = a^{2} - 2 a b + b^{2}

Square of a trinomial

(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a

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}

Sum of cubes

a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})

Difference of cubes

a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})

Difference of nth powers

a^{n} - b^{n} = (a - b) (a^{n - 1} + a^{n - 2} b + \dots + a b^{n - 2} + b^{n - 1})

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