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Question
Simplify `(155 xx 155 xx 155 - 55 xx 55 xx 55)/(155 xx 155 + 155 xx 55 + 55 xx 55)`
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Solution
`(155 xx 155 xx 155 - 55 xx 55 xx 55)/(155 xx 155 + 155 xx 55 + 55 xx 55)`
`= (155^3 - 55^3)/(155^2 + 155 xx 55 = 55^2)`
`= ((155 - 55)(155^2 + 155 xx 55 + 55^2))/(155^2 + 155 xx 55 + 55^2)` `[∵ a^3 - b^3 = (a - b)(a^2 + ab + b^2)]`
= (155 - 55) = 100
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