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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.

User Guide

Welcome to nubtrek.

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.

User Guide

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.

User Guide

nub is the simple explanation of the concept.

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

User Guide

trek is the step by step exploration of the concept.

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.

User Guide

jogger provides the complete mathematical definition of the concepts.

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.

User Guide

exercise provides practice problems to become fluent in the concepts.

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.

summary of this topic

### Polynomial Arithmetics

Voice

Voice

Home

»  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

### Addition and Subtraction of Polynomials

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

• 2xx(3^2)

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

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

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'

Progress

Progress

What is the sum 3 power 2 plus 3 power 2?
times;3;2;power
2 times, 3 power 2
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
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
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"
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