if x,y,z are in A.P., then find the value (x+y-z)(-x+y+z)
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if x,y,z are in AP then
y-x=z-y---------(1) from (1) x=2y-z
(x+y-z)(-x+y+z)
[(2y - z) + y - z][y+ z - (2y - z)]
= (2y - z + y - z)(y+ z - 2y + z)
= (3y - 2z)(2z - y)
= 6yz - 3y - 4z + 2yz
= 8yx - 3y - 4z
y-x=z-y---------(1) from (1) x=2y-z
(x+y-z)(-x+y+z)
[(2y - z) + y - z][y+ z - (2y - z)]
= (2y - z + y - z)(y+ z - 2y + z)
= (3y - 2z)(2z - y)
= 6yz - 3y - 4z + 2yz
= 8yx - 3y - 4z
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