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Simplify each of the following:(i) x2 – 3x + 5 – 1/2(3x2 – 5x + 7)(ii) [5 – 3x + 2y – (2x – y)] – (3x – 7y + 9)(iii) 11/2x2y – 9/4xy2 + 1/4xy – 1/14y2x + 1/15yx2 + 1/2xy |
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Answer» (i) x2 – 3x + 5 – 1/2(3x2 – 5x + 7) = x2 – 3/2x2 – 3x + 5/2x + 5 – 7/2 = (2x2 – 3x2)/2 – (6x + 5x)/2 + (10-7)/2 = -1/2x2 – 1/2x + 3/2 (ii) [5 – 3x + 2y – (2x – y)] – (3x – 7y + 9) = 5 – 3x + 2y – 2x + y – 3x + 7y – 9 = – 3x – 2x – 3x + 2y + y + 7y + 5 – 9 = -8x + 10y – 4 (iii) 11/2x2y – 9/4xy2 + 1/4xy – 1/14y2x + 1/15yx2 + 1/2xy = 11/2x2y + 1/15x2y – 9/4xy2 – 1/14xy2 + 1/4xy + 1/2xy = (165x2y + 2x2y)/30 + (-126xy2 – 4xy2)/56 + (xy + 2xy)/4 = 167/30x2y – 130/56xy2 + 3/4xy = 167/30x2y – 65/28xy2 + 3/4xy |
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