How to Multiply Binomials

Step-by-Step Guide

1. 1

   Step 1: Understand math vocabulary and question types.

   It will be impossible to solve the questions on your next test if you don't know what they are asking.
   
   Luckily, the terminology is not incredibly hard:
   Terms:
   A term is simply a part of the equation being added or subtracted.
   
   It can be a constant, variable, or both.
   
   For example, in 12 + 13x + 4x2, the terms are 12, 13x, and 4x2.
   
   Binomial:
   This is just a complicated way to say "an expression with two terms," like x+3 or x4
   - 3x.
   
   Powers: this refers to an exponent on a term.
   
   For example, we could say that x2 is "x to the second power." Any question asking you to "Find the terms of two binomials (x+3)(x+2)," "find the product of two binomials," or "expand the two binomials" is asking you to multiply binomials.
2. 2

   Step 2: Learn the acronym FOIL to remember the order of binomial multiplication.

   FOIL is a simple guide for multiplying two binomials.
   
   FOIL stands for the order you need to multiply the parts of the binomials together:
   F is for First, O is for Outer, I is for Inner, and L is for Last.
   
   The names refer to the order in which the terms are written.
   
   Let's say we are multiplying the binomials (x+2) and (x+5).
   
   The terms would be:
   First: x & x Outer: x & 5 Inner: 2 & x Last: 2 & 5 , This is the "F" of FOIL.
   
   In our example, (x+2)(x+5), the first terms are "x" and "x." Multiply these together and jot down the answer: "x2." First Term: x * x = x2 , These are two outermost "ends" in our problem.
   
   So, in our example (x+2)(x+5), they would be "x" and "5." Together they make "5x" Outer Term: x * 5 = 5x , The two numbers closest to the center will be your inner term.
   
   For (x+2)(x+5), this means you multiply "2" and "x" to get "2x." Inner Term: 2 * x = 2x , This does not mean the last two numbers, but rather the last number in each parentheses.
   
   So, for (x+2)(x+5), we multiply the "2" and the "5" to get "10." Last Term: 2 * 5 = 10 , Combine the terms by adding them together to create a new, larger expression.
   
   From our previous example, we get the equation: x2 + 5x + 2x + 10 , Like terms are parts of the equation that have the same variable and power.
   
   In our example, the terms 2x and 5x both share an x, and can be added together.
   
   No other terms are alike, so they stay put.
   
   Final Answer: (x+2)(x+5) = x2 + 7x + 10 Advanced Note:
   To learn how like terms work, remember the basics of multiplication. 3 * 5, for example, means that you are adding three fives together to get 15 (5 + 5 + 5).
   
   In our equation, we have 5 * x ( x + x + x + x + x) and 2 * x (x + x).
   
   If we add all the "x"s in the equation we get seven "x"s, or 7x. , When a number is being subtracted, it is the same as adding a negative number.
   
   If you forget to keep the minus sign throughout your calculations you will end up with the wrong answer.
   
   Take the example (x+3)(x-2):
   First: x * x = x2 Outer: x *
   -2 =
   -2x Inner: 3 * x = 3x Last: 3 *
   -2 =
   -6 Add all terms together: x2
   - 2x + 3x
   - 6 Simplify to final answer: x2 + x
   - 6
3. 3

   Step 3: Multiply the FIRST part in each parentheses.

4. 4

   Step 4: Multiply the OUTER parts in each parentheses.

5. 5

   Step 5: Multiply the INNER parts in each parentheses.

6. 6

   Step 6: Multiply the LAST parts in each parentheses.

7. 7

   Step 7: Add all of the new terms together.

8. 8

   Step 8: Simplify like terms.

9. 9

   Step 9: Remember that subtracted numbers are negative.

Detailed Guide

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