Subtraction of polynomials is very much similar to addition of them. We can simply say that

## " The subtraction of one polynomial from the second polynomial is a process of adding the second polynomial into the first polynomial with all the signs of the first polynomial inverted. "

Do not worry if you are unable to understand the above statement. We present a few examples of polynomial subtraction below, and they will make the above idea clear to you:

Here the given statement requires you to evaluate 7x - 4x which is equivalent to finding 7x + (-4x)

We can combine the two like terms through simple subtraction:

=> 7x - 4x = (7 - 4) x = 3x

Due to the sign of **subtraction**, we invert the signs of all the terms present inside the parentheses of the second polynomial as shown below:

`(4x^2 + xy) - (3x^2 + 7xy)`

`= 4x^2 + xy - 3x^2 - 7xy`

` = 4x^2 - 3x^2 + xy- 7xy `

`= (4 - 3)x^2 + (1 - 7)xy`

= ` x^2 - 6xy `

**Again,**
we invert the signs of all the terms present inside the parentheses of the second polynomial while taking them out of the parentheses:

= ` 5x^3 + 3x^2y + 4xy - 6y^2 - 3x^2 - 7x^2y + 2xy - 4xy^2 + 5 `

(Combining like terms just like we did during addition)

= `5x^3 - 3x^2 + (3x^2y - 7x^2y) + (4xy + 2xy) - 6y^2 - 4xy^2 + 5`

= ` 5x^3 - 3x^2 - 4x^2y + 6xy + 2xy - 6y^2 - 4xy^2 + 5`

Hence just like addition process, only like terms can be subtracted from each other.

Just like the addition of two polynomials, we can subtract polynomials through both **"vertical"** and **"horizontal"** methods. We have presented the horizontal method above, and we include an example of vertical method below:

Using the **vertical method,**

We place the like terms above and below each other.

**Note:** In the horizontal method of polynomial subtraction, we saw that due to the -ve sign present before the 2nd polynomial, all the signs inside the parentheses got inverted. In a similar fashion, we need to invert all the signs in the lower polynomial.

`2x^3 + 4x^2 + 3x - 2`

` - 1x^3 - 5x^2 - 9x + 3`

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(Inverting the signs)

`2x^3 + 4x^2 + 3x - 2 `

` - 1x^3 + 5x^2 + 9x - 3`

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` x^3 + 9x^2 + 12x - 5 `

You may choose any of the two methods discussed above. Just make sure that you do not wrongly use the +ve and -ve signs.

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