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

**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

____________________

- Polynomials
- Adding polynomials (+)
- Subtracting polynomials (-)
- Multiplying polynomials (x)
- Dividing polynomials (÷)
- Factoring polynomials
- Factoring quadratic equation
- Word problems using quadratic equation
- Practical problems using quadratic equation
- identities
- Formulas in algebra

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