How do you FOIL a math problem witha binomial and a trinomial?

Answer 1

FOIL is an acronym standing for first, outside, inside, and last, which is a method for multiplying binomials For example: (a + b)(a + b) F (a + b)(a + b) = a2

O (a + b)(a + b) = +ab

I (a + b)(a + b) = +ab

L (a + b)(a + b) = b2 a2 + ab + ab + b2 = a2 + 2ab + b2 *always remember to watch the signs. If you multiply -a times b you get -ab. Also, remember to add or subtract the coefficients (Coefficients are the numbers in front of the variables. If no number is seen, it is automatically a 1. The coefficient of -ab is -1 and the coefficient of ab is 1, thus ab + ab = 2ab). Multiplying binomials and trinomials is similar, but FOIL is not used. There are various methods used, here is one of them: Example 1 (x + 3)(x2 - 3x - 5) Step 1: Multiply x by the entire trinomial (x + 3)(x2 - 3x - 5) = x3

(x + 3)(x2 - 3x - 5) = -3x2

(x + 3)(x2 - 3x - 5) = -5x Step 2: Multiply 3 by the entire trinomial. Remember to keep the signs, or in other words, remember that 3 is positive. (x + 3)(x2 - 3x - 5) = +3x2

(x + 3)(x2 - 3x - 5) = -9x

(x + 3)(x2 - 3x - 5) = -15 The product looks like: x3 - 3x2 - 5x + 3x2 - 9x - 15 Step 3: Combine like terms or simplify x3 - 14x - 15 Remember that terms are ordered by the highest power to the lowest power. Example 2

(2y - 3)(y2 + 6y + 10) Step 1: (2y - 3)(y2+ 6y + 10) = 2y3

(2y - 3)(y2 + 6y + 10) = +12y2

(2y - 3)(y2 + 6y + 10) = +20y Step 2: (2y - 3)(y2 + 6y + 10) = -3y2

(2y - 3)(y2 + 6y + 10) = -18y

(2y - 3)(y2 + 6y + 10) = -30 = 2y3 + 12y2 + 20y - 3y2 - 18y - 30

Step 3: 2y3 + 9y2 + 2y - 30