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Question
Simplify the following products:
`(m + n/7)^3 (m - n/7)`
Solution
We have
`(m + n/7)^3 (m - n/7)`
`= (m + n/7)(m + n/7)(m + n/7)(m - n/7)`
`= (m + n/7)^2 ((m)^2 - (n/7)^2)` `[∵ (a + b)(a + b) = (a + b)^2 & (a + b)(a - b) = a^ - b^2 ]`
`= (m + n/7)^2 [m^2 - n^2/49]`
`∴ (m + n/7)^3(m - n/7) = (m = n/7)^2 [m^2 - n^2/49]`
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