Multiplying a polynomial by a polynomial

To multiply a polynomial by a polynomial, we multiply every term of the first polynomial by every term of the second and add the products. The rule is visible in rectangle areas: a rectangle with sides (a + b) and (c + d) splits into four smaller rectangles with areas ac, ad, bc, bd, so (a + b)(c + d) = ac + ad + bc + bd. After multiplying we combine like terms and write the result in standard form. For three or more polynomials we multiply two at a time. Signs and the number of products (binomial × binomial = 4 products) help check the work.