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Question
Expand the following:
`(5x + 1/x)^2`
Sum
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Solution
Given: `(5x + 1/x)^2`
Step-wise calculation:
1. Use the identity (a + b)2 = a2 + 2ab + b2, where a = 5x and `b = 1/x`.
2. Calculate each term:
a2 = (5x)2 = 25x2
`2ab = 2 xx 5x xx 1/x`
2ab = 2 × 5
2ab = 10
Since `x xx 1/x = 1`
`b^2 = (1/x)^2`
`b^2 = 1/x^2`
3. Add all terms together:
`(5x + 1/x)^2 = 25x^2 + 10 + 1/x^2`
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