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Question
Simplify (2x + p - c)2 - (2x - p + c)2
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Solution
We have
`(2x + p - c)^2 - (2x - p + c)^2`
`= [(2x)^2 + (p)^2 + (-c)^2 + 2(2x)(p) + 2(p)(-c) + 2(2x)(-c)] - [(2x)^2 + (-p)^2 + c^2 + 2(2x)(-p) + 2(2x)(c) + 2(-p)c]`
` =[4x^2 + p^2 + c^2 + 4xp - 2pc - 4cx] - [4x^2 + p^2 + c^2 - 4xp - 2pc + 4cx]`
`= 4x^2 + p^2 + c^2 + 4xp - 2pc - 4cx - 4x^2 - p^2 - c^2 + 4xp + 2pc - 4cx`
= 8xp - 8xc
= 8x(p - c)
`∴ (2x + p - c)^2 - (2x - p + c)^2 = 8x(p - c)`
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