Maths-
General
Easy

Question

Consider the difference of squares π‘Ž2 βˆ’ 𝑏2 for integers π‘Ž and 𝑏. Make a table for the difference of squares using consecutive integers for π‘Ž and 𝑏. What pattern do you notice? Using the pattern find the pair of consecutive integers that generate the difference of squares of –45.

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: 22 and 23


    a and b are consecutive integers. Let’s make a table for some pairs of a and b


    We can notice that the difference of square of consecutive integers a and b is of the form -(a + b).
    If the difference of two consecutive numbers is -45. We can think that there is only one case when a and b in -(a + b) is connective i.e. when a = 22 and b = 23.
    Final Answer:
    Hence, the pattern for difference of squares using consecutive integers for π‘Ž and 𝑏 is -(a + b) and the pair of consecutive integers that generate the difference of squares of –45 is 22 and 23

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