Well, not exactly THAT kind of foil...though it definately comes to mind!
A Binomial is an expression that has two terms. "Bi"- means two and "-nomial" means terms. So a binomial is an expression with two terms.
For example: (3x + 5)(4x + 2) has two binomials. The first one is (3x + 5) and the second one is (4x + 2).
In order to multiply the two binomials together we need to use something called FOIL.
Well, not exactly THAT kind of foil...though it definately comes to mind!
In Math, the term FOIL is used to help you remember the steps used to multiply the two binomials. Each letter in FOIL stands for a step in the calculation.
After using FOIL, we will need to simplify the expression by combining like terms.
Example: Multiply (x + 5)(x + 4)
F: multiply the first terms in each set of parentheses together:
x・x = x2
O: multiply the outer terms together: x・4 = 4x
I: multiply the inside two terms together: 5・x = 5x
L: multiply the last two terms together: 5・4 = 20
Now add each piece together: F + O + I + L
x2 + 4x + 5x + 20
The only set of like terms are the 4x and 5x which combine to make 9x.
The answer is: x2 + 9x + 20
Example:
Multiply (x + 3)(x + 6)
F: x・x = x2
O: x・6 = 6x
I: 3・x = 3x
L: 3・6 = 18
Now add all the terms together: F + O + I + L
x2 + 6x + 3x + 18
Combine like terms: x2 + 9x + 18 *Answer
Example:
Multiply (x + 2)(x + 10)
F: x・x = x2
O: x・10 = 10x
I: 2・x = 2x
L: 2・10 = 20
Now add all the terms together: F + O + I + L
x2 + 10x + 2x + 20
Combine like terms: x2 + 12x + 20 *Answer
Example:
Multiply (x - 4)(x + 5)
F: x・x = x2
O: x・5 = 5x
I: -4・x = -4x
L: -4・5 = -20
Now add all the terms together: F + O + I + L
x2 + 5x + -4x + -20
Combine like terms: x2 + 1x + -20
Simplify: x2 + x - 20 *Answer
Example:
Multiply (x - 7)(x + 1)
F: x・x = x2
O: x・1 = 1x
I: -7・x = -7x
L: -7・1 = -7
Now add all the terms together: F + O + I + L
x2 + 1x + -7x + -7
Combine like terms: x2 + -6x + -7
Simplify: x2 - 6x - 7 *Answer
Example:
Multiply (x + 2)(x - 4)
F: x・x = x2
O: x・-4 = -4x
I: 2・x = 2x
L: 2・-4 = -8
Now add all the terms together: F + O + I + L
x2 + -4x + 2x + -8
Combine like terms: x2 + -2x + -8
Simplify: x2 - 2x - 8 *Answer
Example:
Multiply (x - 6)(x - 8)
F: x・x = x2
O: x・-8 = -8x
I: -6・x = -6x
L: -6・-8 = 48
Now add all the terms together: F + O + I + L
x2 + -8x + -6x + 48
Combine like terms: x2 + -14x + 48
Simplify: x2 - 14x + 48 *Answer
Example:
Multiply (x - 5)(x - 3)
F: x・x = x2
O: x・-3 = -3x
I: -5・x = -5x
L: -5・-3 = 15
Now add all the terms together: F + O + I + L
x2 + -3x + -5x + 15
Combine like terms: x2 + -8x + 15
Simplify: x2 - 8x + 15 *Answer
So how do you know you got the right answer? How do you check your answer?
Pick any value to be x. It doesn't matter which number you choose, just pick a random number. Keep it smaller so the calculation is easier;be nice to yourself!
Step 1: Use substitution of the value you picked into the original problem. Use PEMDAS to calculate the answer.
Step 2: Use substitution into the foiled answer using the same value. Use PEMDAS to calculate the answer.
*You should get the same value for both calculations. This means you did the problem correctly.
For example, the first problem we did together was
(x + 5)(x + 4) which equaled x2 + 9x + 20.
I will choose the number 2 as x. Substitute x = 2 into each equation.
Equation #1: (x + 5)(x + 4)
(2 + 5)(2 + 4) = (7)(6) = 42
Equation #2: x2 + 9x + 20
(2)2 + 9(2) + 20
4 + 18 + 20
22 + 20
42
Notice both problems give us the same solution. So we know we got the correct answer.
What if I tried a different value for x, like x = 6? Repeat the steps above by substituting 6 for x:
Equation #1: (x + 5)(x + 4) = (6 + 5)(6 + 4) = (11)(10) = 110
Equation #2: x2 + 9x + 20
(6)2 9(6) + 20
36 + 54 + 20
90 + 20
110
Notice the two answers are the same again. You can choose any number for x that you want to check your answer. The smaller the value of x is, the easier the computation is. You could use x = 2 to check every problem and that would be okay.
Now you try:
Multiply (x + 5)(x + 7)
Use the caret key (^) to type in the exponent.
Enter your answer and then click submit to see if you got it right.
Now you try:
Multiply (x + 2)(x + 10)
Use the caret key (^) to type in the exponent.
Enter your answer and then click submit to see if you got it right.
Now you try:
Multiply (x - 8)(x + 3)
Use the caret key (^) to type in the exponent.
Enter your answer and then click submit to see if you got it right.
Now you try:
Multiply (x - 10)(x - 2)
Use the caret key (^) to type in the exponent.
Enter your answer and then click submit to see if you got it right.