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Thought-Process to Discover Knowledge

Welcome to **nub****trek**.

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

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

Welcome to **nub****trek**.

The content is presented in small-focused learning units to enable you to

think,

figure-out, &

learn.

**Just keep tapping** (or clicking) on the content to continue in the trail and learn. continue

The content is presented in small-focused learning units to enable you to

think,

figure-out, &

learn.

To make best use of nubtrek, understand what is available.

nubtrek is designed to explain mathematics and science for young readers. Every topic consists of four sections.

nub,

trek,

jogger,

exercise.

This captures the small-core of concept in simple-plain English. The objective is to make the learner to think about. continue

Trekking is bit hard, requiring one to sweat and exert. The benefits of taking the steps are awesome. In the trek, concepts are explained with exploratory questions and your thinking process is honed step by step. continue

This captures the essence of learning and helps one to review at a later point. The reference is available in pdf document too. This is designed to be viewed in a smart-phone screen. continue

This part does not have much content as of now. Over time, when resources are available, this section will have curated and exam-prep focused questions to test your knowledge. continue

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Polynomial Addition and Subtraction

» Numerical expressions can be added or subtracted

→ eg : `[3^4+3^2]``+ [4(3^2)-7]` `=3^4+5(3^2)-7`

→ eg: `[2^3+3(2^2)]` `-[2^3+2(2^2)-5]` `=2^2+5`

» In Polynomials, like terms get added or subtracted

→ eg : `[x^4+x^2]``+ [4(x^2)-7]` `=x^4+5(x^2)-7`

→ eg: `[y^3+3(y^2)]` `-[y^3+2(y^2)-5]` `=y^2+5`

→ eg : `3x^2y + 2x^2y` `=5x^2y`

→ eg : `3x^2y - 2x^2y` `=x^2y`

→ eg : `3x^2y + 2xy^2` cannot be further simplified

*plain and simple summary*

nub

*plain and simple summary*

nub

dummy

In polynomial addition or subtraction, like terms are combined.

*simple steps to build the foundation*

trek

*simple steps to build the foundation*

trek

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

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

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

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 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`
- 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`

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
- similar terms

The answer is 'like terms'

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

- subtraction is not possible
- `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`

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`

*comprehensive information for quick review*

Jogger

*comprehensive information for quick review*

Jogger

dummy

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

*practice questions to master the knowledge*

Exercise

*practice questions to master the knowledge*

Exercise

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

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

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

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

The answer is 'both the above'

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+1`

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

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`

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

*your progress details*

Progress

*About you*

Progress

What is the sum 3 power 2 plus 3 power 2?

times;3;2;power

2 times, 3 power 2

exponents;cannot;added

exponents cannot be added

The answer is "2 times, 3 power 2". Numerical expressions of exponents can be added.

What is the sum 2 times 3 powe 3, + 5 times 3 power 3, + 5 times 3 power 2?

12

12 times, 3 power 3

7;5

7 times 3 power 3 plus 5 times 3^2

The answer is "7 times 3 power 3 plus 5 times 3^2"

Given 2 times 3 power 3, + 5 times 3 power 3, + 5 times 3 power 2; the result is 7 times 3 power 3 plus 5 times 3^2. Only if the numerical value of 3 power 3 is substituted the numerical expression can further be simplified.;; In a similar algebraic expression with variable x, the two terms x cube and x squared cannot be combined with addition or subtraction. Algebraic expressions and polynomials are representation of numerical quantities using variables.

What is the sum 3 x power 7 plus 2 x power 7?

5;7;power

5 x power 7

terms;cannot;added

terms cannot be added

The answer is "5 x power 7"

What is the sum of 3 x squared + 2x and 7 x squared minus 3x minus 2?

9

9 x squared x

11;minus;2

10 x squared minus x minus 2

The answer is "10 x squared minus x minus 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

like terms

similar

similar terms

The answer is 'like terms'

Which of the following is an equivalent expression if 3 power 3 minus 5 is subtracted from 5 times 3 power 3, + 5 times 3 power 2?

subtraction;not;possible

subtraction is not possible

4;times;3;5;2

4 times 3 power 3 + 5 times 3 power 2 + 5

The answer is "4 times 3 power 3 + 5 times 3 power 2 + 5"

Subtract 3 x squared + 2 x from 7 x squared minus 3 x minus 2.

9

9 x squared x minus 2

4;minus;5

4 x squared minus 5 x minus 2

The answer is "4 x squared minus 5 x minus 2"

Subtraction is shown in this page.

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.

What is the sum of the given polynomials?

1

2

The answer is "the second option"

What is the sum of the given polynomials?

1

2

3

The answer is 'both the above'

What is the difference of the given two polynomials?

1

2

3

The answer is "second option"

What is the difference of the given two polynomials?

1

2

3

The answer is "third option"