Polynomials

Monomial:    Single term expression    ex. 4ab
Binomial:    Two termed expression    ex. x + 2
Trinomial:    Three termed expression    ex.    x² - 4x + 4
Like Terms:    Two terms with the same variable expression    ex.    4x² and -10x²
Unlike Terms:    Two terms without the same variable expression    ex.    4x and 4x² (the powers differ)
Adding: Combine like terms.    ex.    4ab + (-6cd) + 7ab + 8cd = 11ab + 2cd
Subtracting:    Add the opposite of the second polynomial    ex.    x² - (3x² + 4x -5) =
                                                                                                     x² - 3x² - 4x +5 = -2x² - 4x +5
Multiplying:
    A monomial by a polynomial:    Multiply through using the distributive property
                                                        ex.    x(3x + 2) = 3x² + 2x
    A Binomial by a Binomial:    Use FOIL   (First    Outer    Inner    Last)
                                       ex. (x - 2)(x + 4) = (x)(x) + (x)(4) + (x)(-2) + (-2)(4) = x² + 4x - 2x - 8
                                                                                                                = x² +2x - 8
Dividing:    A polynomial by a monomial; divide each term by the monomial
                ex. 15y⁴ - 12xy³divided by 3y² = 15y⁴/3y² - 12xy³/3y² = 5y² - 4xy