बहुपद 7x2−4xy+8y2+5x−3y7x^2 - 4xy + 8y^2 + 5x - 3y और 5x2−4y2+6y−35x^2 - 4y^2 + 6y - 3 का अन्तर होगा :

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A.4x2−2xy+12y2+5x−9y+34x^2 - 2xy + 12y^2 + 5x - 9y + 3
B.2x2−4xy+12y2+5x−9y+32x^2 - 4xy + 12y^2 + 5x - 9y + 3सही
C.2x2−4xy−12y2+5x−9y+32x^2 - 4xy - 12y^2 + 5x - 9y + 3
D.4x2−2xy−12y2−5x+9y−34x^2 - 2xy - 12y^2 - 5x + 9y - 3
व्याख्या एवं हल

सही उत्तर: (B) 2x^2 - 4xy + 12y^2 + 5x - 9y + 3

पहले बहुपद में से दूसरे बहुपद को घटाने पर: (7x^2 - 4xy + 8y^2 + 5x - 3y) - (5x^2 - 4y^2 + 6y - 3) = 2x^2 - 4xy + 12y^2 + 5x - 9y + 3 प्राप्त होता है।

In English (Question & Model Answer)

Difference between polynomials 7x2−4xy+8y2+5x−3y7x^2 - 4xy + 8y^2 + 5x - 3y and 5x2−4y2+6y−35x^2 - 4y^2 + 6y - 3 is :

A.4x2−2xy+12y2+5x−9y+34x^2 - 2xy + 12y^2 + 5x - 9y + 3
B.2x2−4xy+12y2+5x−9y+32x^2 - 4xy + 12y^2 + 5x - 9y + 3Correct
C.2x2−4xy−12y2+5x−9y+32x^2 - 4xy - 12y^2 + 5x - 9y + 3
D.4x2−2xy−12y2−5x+9y−34x^2 - 2xy - 12y^2 - 5x + 9y - 3

Correct Answer: (B) 2x^2 - 4xy + 12y^2 + 5x - 9y + 3

Subtracting the second polynomial from the first: (7x^2 - 4xy + 8y^2 + 5x - 3y) - (5x^2 - 4y^2 + 6y - 3) = (7-5)x^2 - 4xy + (8 - (-4))y^2 + 5x + (-3 - 6)y - (-3) = 2x^2 - 4xy + 12y^2 + 5x - 9y + 3.

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