Math 8 Special Products Lecture

This set of vocabulary flashcards covers the formulas and definitions for various special products in Algebra as presented by Ms. Olivia A. Tura.

FOIL Method

A technique used for finding the product of two binomials by multiplying the first terms, outer terms, inner terms, and last terms.

Square of a Binomial (Formula)

$$(1st)^2 \times 2(1st)(2nd) + (2nd)^2$$

Product of Sum and Difference of Two Terms (Formula)

$(x + y)(x - y) = x^2 - 9$ in sample calculations, generally $(x + y)(x - y) = x^2 - y^2$

Special Products

A set of six specific algebraic categories: Product of Two Binomials, Product of Sum and Difference of Two terms, Square of a Binomial, Cube of a Binomial, Square of a Trinomial, and Product of a Binomial and a Trinomial.

Cube of a Binomial (Definition)

Equal to the cube of the first term plus thrice the product of the second term and the square of the first term plus thrice the product of the first term and the square of the second term plus the cube of the second term.

Cube of a Binomial (Formulas)

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

Square of a Trinomial (Definition)

Equal to the sum of the squares of each term in the trinomial plus twice the product of the first and second term plus twice the product of the first and third term plus twice the product of the second and third term.

Square of a Trinomial (Formula)

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

Product of a Binomial and a Trinomial (Definition)

The product of a binomial $(x + y)$ and a trinomial $(x^2 - xy + y^2)$ is simply equal to the sum of the cubes of the first term and second term of the binomial.

Product of a Binomial and a Trinomial (Formulas)

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

Written Work #3 Date

Friday, July 31, 2026, covering the topic of Special Products.