J's answer to charissa's Secondary 2 Maths Singapore question.
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The result is 20n, which means it is the product of 20 and n. In other words, it is a multiple of 20 since it is 20 × n.
So for all n, (5n + 1)² - (5n - 1)² is a multiple of 20.
Alternative way to show the working without expanding both terms : use the property a² - b² = (a + b)(a - b)
(5n + 1)² - (5n - 1)² = (5n + 1 + (5n - 1))(5n + 1 - (5n - 1))
= (5n + 1 + 5n - 1)(5n + 1 - 5n + 1)
= (10n)(2)
= 20n
The result is 20n, which means it is the product of 20 and n. In other words, it is a multiple of 20 since it is 20 × n.
So for all n, (5n + 1)² - (5n - 1)² is a multiple of 20.
Alternative way to show the working without expanding both terms : use the property a² - b² = (a + b)(a - b)
(5n + 1)² - (5n - 1)² = (5n + 1 + (5n - 1))(5n + 1 - (5n - 1))
= (5n + 1 + 5n - 1)(5n + 1 - 5n + 1)
= (10n)(2)
= 20n
Date Posted:
3 years ago
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