Maths-
General
Easy

Question

Use the product of sum and difference to find 83 × 97.

Hint:

The methods used to find the product of binomials are called special products.
Difference of squares is a case of a special product which occurs when we multiply a binomial by another binomial with the same terms but the opposite sign

The correct answer is: 8051.


    83 can be written as (90 - 7) and 97 can be written as (90 + 7)
    So, 83 × 97 can be written (90 - 7) ×  (90 + 7)
    (90 - 7) ×  (90 + 7)  = 90(90 + 7) - 7(90 + 7)

    =  90(90) + 90(7) - 7(90) - 7(7)

    = 8100 + 630 - 630 - 49

    = 8100 - 49

    = 8051
    Final Answer:
    Hence, the simplified form of 83 × 97 is 8051.
     

    This question can be easily solved by using the formula
    (a + b)(a - b) = a2 - b2

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