simplify
(x+y-z)+(3x-5y+7z)-(14x+7y-6z)
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(i) (x + y – z) + (3x – 5y + 7z) – (14x – 7y – 6z) = (x + y – z) + (3x – 5y + 7z) + (-14x – 7y + 6z) = (x + 3x – 14x) + (y – 5y – 7y) + (-z + 7z + 6z) = (1 + 3 – 14)x + (1 – 5 – 7)y + (-1 + 7 + 6)z = – 10x – 11y + 12z (ii) p + p + 2 + 3 – p – 4 – p – 5 + p + 10 = (p + p + p – p – p + p) + (2 + 3 – 4 – 5 + 10) = (1 + 1 + 1 – 1 – 1 + 1)p + 6 = 2p + 6 (iii) n + (m + 1) + (n + 2) + (m + 3) + (n + 4) + (m + 5) = n + m + 1 + n + 2 + m + 3 + n + 4 + m + 5 = n + n + n + m + m + m + 1 + 2 + 3 + 4 + 5 = (1 + 1 + 1)n + (1 + 1 + 1)m + 15 = 3n + 3m + 15 = 3m + 3n +
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