__maths__>__Introduction to Algebra, Polynomials, and Identities__>__Polynomial Arithmetics__### Addition and Subtraction of Polynomials

In this page, addition and subtraction of polynomials are introduced.

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What is the sum of `3^2+3^2`?

- `2xx(3^2)`
- `2xx(3^2)`
- exponents cannot be added

The answer is '`2xx(3^2)`'.*Numerical expressions of exponents can be added.*

What is the sum of `2(3^3)+5(3^3)+5(3^2)`?

- `12xx(3^3)`
- `7(3^3)+5(3^2)`
- `7(3^3)+5(3^2)`

The answer is '`7(3^3)+5(3^2)`'

Given `2(3^3)+5(3^3)+5(3^2)`, the result is `7(3^3)+5(3^2)`. Only if the numerical value of `3^3` is substituted, then the numerical expression can further be simplified.

In a similar algebraic expression with variable `x`, the two terms `x^3` and `x^2` cannot be combined with addition or subtraction. *Algebraic expressions and polynomials are representation of numerical quantities using variables.*

What is the sum of `3x^7+2x^7`?

- `5x^7`
- `5x^7`
- terms cannot be added

The answer is '`5x^7`'

What is the sum of `3x^2+2x` and `7x^2-3x-2`?

- `9x^2 x`
- `10x^2-x-2`
- `10x^2-x-2`

The answer is '`10x^2-x-2`'

It is noted that terms with identical variables and exponent can be combined in addition and subtraction.

What are the terms with identical variables and exponents called?

- like terms
- like terms
- similar terms

The answer is 'like terms'

Which of the following is an equivalent expression to the result of the following? `3^3-5` is subtracted from `5(3^3)+5(3^2)`

- subtraction is not possible
- `4(3^3)+5(3^2)+5`
- `4(3^3)+5(3^2)+5`

The answer is '`4(3^3)+5(3^2)+5`'

`color(coral)(5(3^3)+5(3^2))` `- (color(deepskyblue)(3^3-5))`

`=color(coral)(5(3^3)+5(3^2))` `color(deepskyblue)(- 3^3+5)`

`=(color(coral)(5)-color(deepskyblue)(1))3^3 + color(coral)(5)(3^2)+color(deepskyblue)(5)`

Subtract `3x^2+2x` from `7x^2-3x-2`.

- `9x^2 x-2`
- `4x^2-5x-2`
- `4x^2-5x-2`

The answer is '`4x^2-5x-2`'

Subtract `color(coral)(3x^2+2x)` from `color(deepskyblue)(7x^2-3x-2)`.

`color(deepskyblue)(7x^2-3x-2)` - `(color(coral)(3x^2+2x))`

`= color(deepskyblue)(7x^2-3x-2)` `color(coral)(- 3x^2-2x)`

`= color(deepskyblue)(7x^2) color(coral)(- 3x^2)``color(deepskyblue)(-3x) color(coral)(- 2x)``color(deepskyblue)(-2)`

`= (color(deepskyblue)(7)color(coral)(- 3))x^2``+(color(deepskyblue)(-3) color(coral)(- 2))x``+color(deepskyblue)(-2)`

`=4x^2-5x-2`

In polynomial addition or subtraction, like terms are combined.

**Polynomial Addition and Subtraction** : Like terms of polynomials are added or subtracted to a simplified polynomial as result.

*Solved Exercise Problem: *

What is the sum of the polynomials `-x^3-x` and `2x^2+3`?

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

The answer is '`-x^3+2x^2-x+3`'

*Solved Exercise Problem: *

What is the sum of `-2x^2y+2xy+3` and `-4yx^2+2yx+1`?

- `-6x^2y + 4xy+4`
- `-6yx^2 + 4yx+4`
- both the above
- both the above

The answer is 'both the above'

*Solved Exercise Problem: *

What is difference of polynomials `2x^2-4x+3` minus `x^3-2`?

- `x^2-4x+1`
- `-x^3+2x^2-4x+5`
- `-x^3+2x^2-4x+5`
- `-x^3+2x^2-4x+1`

The answer is '`-x^3+2x^2-4x+5`'

*Solved Exercise Problem: *

What is the difference between polynomials `x^2y-zx` minus `z^2x-yx^2`?

- `3z^2x-zx`
- `-z^2x-zx`
- `2x^2y-z^2x-zx`
- `2x^2y-z^2x-zx`

The answer is '`2x^2y-z^2x-zx`'

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