Subtracting polynomials





Subtracting polynomials is quite similar to addition of polynomials, only thing we have to take care of minus sign. Subtraction can be done both in horizontally and vertically Here we have given two examples on each method in each category we will get the same answer. vertically.

Example 1 :

Subtract the following polynomials:

(2 x³ - 2 x² + 4 x - 3)- (x³ + x² - 5 x + 4)

Step 1:

In the first step we are going to multiply the negative with inner terms.

                    = 2x³ -2x² + 4x -3 - x³-x²+5x-4
Step 2:

In the second step we have to combine the like terms

                   = 2x³ - x³ -2x²-x² + 4x + 5x - 3 - 4
Step 3:

After combining the like terms we will get the answer

                  = x³ + x² + 9x - 7


Example 2 :

Subtract :  (x³ - 5 x² - 2 x - 3)- (3 x³ + 2 x² - 3 x + 9)

Step 1:

In the first step we are going to multiply the negative with inner terms.

                    = x³ - 5 x² - 2 x - 3 - 3 x³ - 2 x² + 3 x - 9
Step 2:

In the second step we have to combine the like terms

                  = x³ - 3 x³ - 5 x²- 2 x² - 2 x + 3 x - 3 - 9
Step 3:

After combining the like terms we will get the answer

                  = -2x³ - 3x² + x - 12


Example 3 :

Subtract :  (x³ - x² - 3 x)- (3 x³ + 2 x² + 9)

Step 1:

In the first step we are going to multiply the negative with inner terms.

                    = x³ - x² - 3 x - 3 x³ - 2 x² - 9
Step 2:

In the second step we have to combine the like terms

                  = x³ - 3 x³ - x²- 2 x² -  3 x - 9
Step 3:

After combining the like terms we will get the answer

                  = -2 x³ - 3 x² - 3 x - 9


Horizontal method of Subtracting polynomials:

Example 1 :

Subtract:  (2 x³ -2 x² + 4 x - 3)-(x³ + x² - 5 x + 4)

We have to change the original symbol of the

                                       2x³ -2x² + 4x -3
                                       x³ + x² - 5x + 4
                                       (-)   (-)   (+)   (-)
                                  ____________________
                                     3x³ - 3x ² + 9x - 7
                                  ____________________


Example 2 :

Subtract: (x³- 5 x² - 2 x - 3)-(3 x³ + 2 x² - 3 x + 9)

We have to change the original symbol of the

                                 x³ - 5 x² - 2 x - 3
                               3x³ + 2x² - 3x + 9
                               (-)    (-)     (+)    (-)
                            ____________________
                             -2x³ - 7x ² + x - 12
                             ____________________


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