Types of Special Products

Vocabulary flashcards covering the seven types of special products and their corresponding algebraic formulas.

Special Products

Products of polynomials with special forms of factors that can be obtained easily using special product formulas.

Type 1: The Distributive Property of Multiplication over Addition or Subtraction

The formula $x(a \pm b) = ax \pm bx$

Type 2: Product of Two Binomials – FOIL

The formula $(ax + by)(cx + dy) = acx^2 + (ad + bc)xy + bdy^2$

Type 3: Square of Binomial (Sum)

The formula $(x + y)^2 = x^2 + 2xy + y^2$

Type 3: Square of Binomial (Difference)

The formula $(x - y)^2 = x^2 - 2xy + y^2$

Type 4: Product of the Sum and Difference of the Same Two Terms

The formula $(x + y)(x - y) = x^2 - y^2$

Type 5: Cube of Binomial (Sum)

The formula $(x + y)^3 = x^3 + 3x^2y + 3xy^2 + y^3$

Type 5: Cube of Binomial (Difference)

The formula $(x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3$

Type 6: Special Case of Product of Binomial and Trinomial (Sum of Cubes)

The formula $(x + y)(x^2 - xy + y^2) = x^3 + y^3$

Type 6: Special Case of Product of Binomial and Trinomial (Difference of Cubes)

The formula $(x - y)(x^2 + xy + y^2) = x^3 - y^3$

Type 7: Square of Trinomial

The formula $(x + y + z)^2 = x^2 + y^2 + z^2 + 2xy + 2yz + 2xz$