Adding Polynomials
2x
3
3 x 4 x 3 x 5 x 2 x 7 2
3
2
Combine Like Terms (Same Variable and Same Exponent)
2 x3 x3 3x 2 5 x 2 4 x 2 x 3 7 (2 1) x 3 (3 5) x 2 ( 4 2) x (3 7) 3 x 3 2 x 2 6 x 4 3x 3 2 x 2 6 x 4
OR
subtracting Polynomials
x
3
2 x 6 x 2 2 x 4 x x 4 2
3
2
Subtraction is the same as adding the opposite so change to add the opposite. 3 2 3 2 x 2 x 6 x 2 2 x 4 x x 4
3 2 3 2 x 2 x 6 x 2 2 x 4 x x 4
Now just combine the like terms.
x 2x 2x 4x 6x x 2 4 3
3
2
2
x 2 x 5x 2 3
2
Multiplying Polynomials
2x 3 4x 5 Multiply the first term times each term in the second parentheses. Then multiply the second term times each term in the second parentheses.
2 x(4 x) 2 x(5) 3(4 x) 3(5) 8 x 2 10 x 12 x 15 8 x 2 2 x 15
Remember to combine the like terms.
Super-sized multiplication
x 3 2 x
2
3x 1
This is the same process. Multiply the first term times each term in the second parentheses. Then multiply the second term times each term in the second parentheses. x(2 x 2 ) x(3x) x(1) 3(2 x 2 ) 3(3x) 3(1) 2 x3 3x 2 x 6 x 2 9 x 3 2x3 9 x 2 8x 3
Remember to combine the like terms.
Special products Remember when you see a binomial like this one just write it down twice and multiply.
2 x 3
2
2 x 3 2 x 3 4x2 6x 6x 9 4 x 2 12 x 9