Server Error

Server Not Reachable.

This may be due to your internet connection or the nubtrek server is offline.

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 IdentitiesBasic Algebraic Identities

### Multiplication Simplified Using Algebraic Identities

The algebraic identities of square can be used to simplify multiplication of numbers or square of numbers.

click on the content to continue..

Which of the following is true to compute 71^2?

• Using (a+b)^2 identity to calculate (70+1)^2
• Using (a+b)^2 identity to calculate (70+1)^2
• algebraic identities cannot be used for numbers

The answer is 'Using (a+b)^2 identity to calculate (70+1)^2'

To compute 71^2 the (a+b)^2 identity is used to simplify the multiplication.
71^2
=(70+1)^2
=70^2+2xx70xx1+1^2
=4900 + 140 + 1
=5041

Solved Exercise Problem:

Compute 52^2 using an algebraic identity.

• (50+2)^2 =2500+200+4
• (50+2)^2 =2500+200+4
• (5+2)^2 =25+20+4

The answer is '(50+2)^2 =2500+200+4'

Which of the following is true to compute 69^2?

• Using (a-b)^2 identity to calculate (70-1)^2
• Using (a-b)^2 identity to calculate (70-1)^2
• algebraic identities cannot be used for numbers

The answer is 'Using (a-b)^2 identity to calculate (70-1)^2'

To compute 69^2 the (a-b)^2 identity is used to simplify multiplication.
69^2
=(70-1)^2
=70^2-2xx70xx1+1^2
=4900 - 140 + 1
=4761

Solved Exercise Problem:

Compute 87^2 using an algebraic identity.

• (90-3)^2 =8100-540+9
• (90-3)^2 =8100-540+9
• (8+7)^2 =64+112+49

The answer is '(90-3)^2 =8100-540+9'

Which of the following is true to compute 73 xx 67?

• Using (a+b)(a-b) identity to calculate (70+3)(70-3)
• Using (a+b)(a-b) identity to calculate (70+3)(70-3)
• algebraic identities cannot be used for numbers

The answer is 'Using (a+b)(a-b) identity to calculate (70+3)(70-3)'

To compute 73xx67 the (a+b)(a-b) identity is used to simplify the multiplication.
73xx67
=(70+3)(70-3)
=70^2-3^2
=4900 -9
=4891

Solved Exercise Problem:

Compute 52xx48 using an algebraic identity.

• (50+2)(50-2) =2500-4
• (50+2)(50-2) =2500-4
• (5+2)48 =5xx48+2 xx 48

The answer is '(50+2)(50-2) =2500-4'

algebraic identity helps to simplify some numerical multiplications.

Using Algebraic Identities in Numerical Multiplication: The variables of algebraic identities can be substituted with numbers and the identities can be used if multiplication becomes simpler.

slide-show version coming soon