InterviewSolution
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InterviewSolution
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If A = 4x2 + y2 – 6xy; B = 3y2 + 12x2 + 8xy; C = 6x2 + 8y2 + 6xy then, find (i) A + B + C (ii) (A – B) – C |
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Answer» Given A = 4x2 + y2 – 6xy; B = 3y2 + 12x2 + 8xy; C = 6x2 + 8y2 + 6xy Write the given expressions in standard form. A = 4x2 – 6xy + y2 B = 12x2 + 8xy + 3y2 C = 6x2 + 6xy + 8y2 (i) A + B + C = (4x2 – 6xy + y2) + (12x2 + 8xy + 3y2) + (6x2 + 6xy + 8y2) = 4x2 – 6xy + y2 + 12x2 + 8xy + 3y2 + 6x2 + 6xy + 8y2 = (4x2 + 12x2 + 6x2 ) + (- 6xy + 8xy + 6xy) + (y2 + 3y2 + 8y2 ) = (4 + 12 + 6) x2 + (- 6 + 8 + 6) xy + (1 + 3 + 8)y2 ∴ A + B + C = 22x2 + 8xy + 12y2 (ii) (A – B) – C A + (- B) + (- C) Additive inverse of B is – B = – (12x2 + 8xy + 3y2 ) ∴ – B = – 12x2 – 8xy – 3y2 Additive inverse of C is – C = -(6x2 + 6xy + 8y2 ) ∴ – C = – 6x2 – 6xy – 8y2 A + (- B) + (- C) = (4x2 – 6xy + y2 ) + (- 12x2 – 8xy – 3y2 ) + (- 6x2 – 6xy – 8y2) = 4x2 – 6xy + y2 – 12x2 – 8xy – 3y2 – 6x2 – 6xy – 8y2 = (42x – 12x2 – 6x2 ) + (- 6xy – 8xy – 6xy) + (y2 – 3y2 – 8y2 ) ∴ (A – B) – C = – 14x2 – 20xy – 10y2 |
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