Multiplying binomials using foil method :
When we multiply two binomials, we use FOIL method
F - First terms
O - Outer terms
I - Inner terms
L - Last terms
Let us look into some examples to understand how we use FOIL method to multiply two binomials.
Example 1 :
Multiply (3x + 2)(x + 3)
Solution :
Here we use FOIL method to multiply the above binomials.
Step 1 :
F | |
O | |
I | |
L |
Step 2 :
Combining the terms
= 3x^{2} + 9x + 2x + 6
= 3x^{2} + 11x + 6
Hence the product of the above binomials is 3x^{2} + 11x + 6
Example 2 :
Multiply (x - 1)(2x - 2)
Solution :
Here we use FOIL method to multiply the above binomials.
Step 1 :
F |
x (2x) = 2x^{(1+1) }= 2x^{2} |
O |
x (-2) = -2x |
I |
-1 (2x) = -2x |
L |
-1 (-2) = 2 |
Step 2 :
Combining the terms
= 2x^{2} - 2x - 2x + 2
= 2x^{2} - 4x + 2
Hence the product of the above binomials is 2x^{2} - 4x + 2
Example 3 :
Multiply (2x + 3)(2x - 3)
Solution :
Here we use FOIL method to multiply the above binomials.
Step 1 :
F |
2x (2x) = 4x^{(1+1) }= 4x^{2} |
O |
2x (-3) = -6x |
I |
3 (2x) = 6x |
L |
+3 (-3) = -9 |
Step 2 :
Combining the terms
= 4x^{2} - 6x + 6x - 9
= 4x^{2} - 9
Hence the product of the above binomials is 4x^{2} - 9
Example 4 :
Multiply (x + 1)(x - 3)
Solution :
Here we use FOIL method to multiply the above binomials.
Step 1 :
F |
x (x) = x^{(1+1) }= x^{2} |
O |
x (-3) = -3x |
I |
1 (x) = x |
L |
+1 (-3) = -3 |
Step 2 :
Combining the terms
= x^{2} - 3x + x - 3
= x^{2} - 2x - 3
Hence the product of the above binomials is x^{2} - 2x - 3
Example 5 :
Multiply (4x + 1)(5x - 8)
Solution :
Here we use FOIL method to multiply the above binomials.
Step 1 :
F |
4x (5x) = 20x^{(1+1) }= 20x^{2} |
O |
4x (-8) = -32x |
I |
1 (5x) = 5x |
L |
+1 (-8) = -8 |
Step 2 :
Combining the terms
= 20x^{2} - 32x + 5x - 8
= 20x^{2} - 27x - 8
Hence the product of the above binomials is 20x^{2} -27x-8
After having gone through the stuff given above, we hope that the students would have understood "Multiplying binomials using foil method".
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