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Question
Simplify the following products:
`(x/2 - 2/5)(2/5 - x/2) - x^2 + 2x`
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Solution
`(x/2 - 2/5)(2/5 - x/2) - x^2 + 2x`
On rearranging we get,
⇒ `(x/2 - 2/5)[-(x/2 - 2/5)] - x^2 + 2x`
⇒ `- (x/2 - 2/5)^2 - x^2 + 2x`
We shall use the identity (x − y)2 = x2 − 2xy + y2
By substituting `x = x/2, y = 2/5`
⇒ `- [(x/2)^2 - 2(x/2)(2/5) + (2/5)^2] - x^2 + 2x`
⇒ `- [x^2/4 - (2x)/5 + 4/25] - x^2 + 2x`
⇒ `- [x^2/4 - (2x)/5 + 4/25] - x^2 + 2x`
⇒ `- x^2/4 + (2x)/5 - 4/25 - x^2 + 2x`
⇒ `- x^2/4 - x^2 - 4/25 + (2x)/5 + 2x`
⇒ `[- x^2/4 - x^2] - 4/25 + [(2x)/5 + 2x]`
⇒ `[- x^2/4 - x^2] - 4/25 + [(2x)/5 + 2x]`
⇒ `[- x^2/4 - (4x^2)/4] - 4/25 + [(2x)/5 + (10x)/5]`
⇒ `[(- x^2 - 4x^2)/4] - 4/25 + [(2x + 10x)/5]`
⇒ `(- 5x^2)/4 - 4/25 + (12x)/5`
Hence, the value of `(- 5x^2)/4 - 4/25 + (12x)/5`.
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