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Thought-Process to Discover Knowledge

Welcome to nubtrek.

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.continue

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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