To multiply two binomials, you may have heard the term "FOIL" for first, outside, inside, last. $\displaylines{(x+2)(x-1) \\ x^2 -1x + 2x -2 \\ x^2 - 3x - 2}$ To multiply two polynomials where at least one has more than two terms, multiply each term in the first polynomial by each term in the second polynomial and combine like terms. $\displaylines{(x^2 + x - 2)(x - 1) \\ x^3 + x^2 + x^2 + x - 2x - 2 \\ x^3 + 2x^2 - x -2}$ To multiply more than two polynomials, repeat the above process taking two polynomials at a time. $\displaylines{(x+2)(x-1)(x+3) \\ (x^2 - 3x - 2)(x+3) \\ x^3 + 3x^2 - 3x^2 - 9x - 2x - 6 \\ x^3 - 11x -6}$ This same logic holds for two variables. $\displaylines{(x+y)^3 \\ (x^2 + 2xy + y^2)(x + y) \\ x^3 + x^2y + 2x^2y + 2xy^2 + xy^2 + y^3 \\ x^3 + 3x^2y + 3xy^2 + y^3}$ Pascal's triangle can be used as a shortcut for exponentiation of $(x+y)$ to any power. To build Pascal's triangle, sum the neighboring terms (with 0 on the outsides). The result will be the coefficients of each term in the expanded polynomial. $1 2 1$ $1 3 3 1$ $1 4 6 4 1$