Maths-
General
Easy
Question
Consider the difference of squares 𝑎2 − 𝑏2 for integers 𝑎 and 𝑏. Make a table for the difference of squares using consecutive integers for 𝑎 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 𝑎 and 𝑏 is -(a + b) and the pair of consecutive integers that generate the difference of squares of –45 is 22 and 23
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 𝑎 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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