Special Products and Factoring (Video Notes)

Vocabulary flashcards covering square of binomial, sum/difference of terms, DOTS, PST, GCMF, SDTC, GT, and factoring concepts from the video notes.

Square of a Binomial

For any numbers a and b, (a ± b)^2 = a^2 ± 2ab + b^2.

Binomial

A polynomial with exactly two terms.

Sum and Difference of Two Terms

(a + b)(a - b) = a^2 − b^2; the product factors into a difference of squares.

Difference of Two Squares (DOTS)

If an expression is a^2 − b^2, it factors as (a + b)(a − b).

DOTS Example: x^2 − 1

x^2 − 1 = (x + 1)(x − 1).

DOTS Example: x^2 − 4y^4

x^2 − 4y^4 = (x − 2y^2)(x + 2y^2).

Perfect Square Trinomial (PST)

A trinomial of the form a^2 ± 2ab + b^2 that factors as (a ± b)^2.

PST Example: x^2 − 4x + 4

x^2 − 4x + 4 = (x − 2)^2.

PST Example: 4x^2 + 12xy + 9y^2

4x^2 + 12xy + 9y^2 = (2x + 3y)^2.

Greatest Common Monomial Factor (GCMF)

The largest monomial factor that divides all terms of a polynomial; factoring it out.

Sum and Difference of Two Cubes (SDTC)

For a^3 ± b^3, factors as (a ± b)(a^2 ∓ ab + b^2).

General Trinomial (GT)

Factoring ax^2 + bx + c by splitting the middle term to factor as a product of binomials.

Factoring

Writing a polynomial as a product of two or more polynomials; the reverse process of polynomial multiplication.

SDTC Example: a^3 − b^3

a^3 − b^3 = (a − b)(a^2 + ab + b^2).