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Thought-Process to Discover Knowledge

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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.



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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.

                            
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