Question: Find multiplication of 198 and 202 using the identity (x+a)(x+b) = x2 + (a+b)x + ab
Answer: In this question, we need to multiply two numbers 198 and 202 by using the standard formulas given in the question.
Let us see how we solve this question. First we need to rewrite the numbers 198 and 202 in such a way that it takes the form of (x+a)(x+b). So, 198 can be written as 200 − 2 or 200 + (-2) and 202 can be written as 200 + 2.
Let us place these values in the formula format. We need to multiply following numbers:
(200 + (−2)) (200 + 2)
In this case x is 200, a is −2, and b is +2. Let us put all together in the equation:
(200 + (-2)) (200 + 2)
= 2002 + ((−2) + 2)200 + (−2)(2)
= 40000 + 0 − 4
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