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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.
mathsIntroduction to Algebra, Polynomials, and IdentitiesPolynomial Arithmetics

### Addition and Subtraction of Polynomials

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

• 2xx(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)
• 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

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

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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