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in Algebraic Expressions by (56.3k points)

From the sum of x+ 3y2 − 6xy, 2x2 − y2 + 8xy, y2 + 8 and x2 − 3xy subtract −3x2 + 4y2 – xy + x – y + 3.

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First we have to find the sum of (x2 + 3y2 – 6xy), (2x2 – y2 + 8xy), (y2 + 8) and (x2 – 3xy)

={(x2 + 3y2 – 6xy) + (2x2 – y2 + 8xy) + ( y2 + 8) + (x2 – 3xy)}

={x2 + 3y2 – 6xy + 2x2 – y2 + 8xy + y2 + 8 + x2 – 3xy}

= {x2+ 2x2+ x2 + 3y2– y2 + y2– 6xy + 8xy – 3xy + 8}

= 4x2 + 3y2 – xy + 8

Now, from the result subtract the −3x2 + 4y2 – xy + x – y + 3

Therefore, required expression = (4x2 + 3y2 – xy + 8) – (- 3x2 + 4y2 – xy + x – y + 3)

= 4x2 + 3y2 – xy + 8 + 3x2 – 4y2 + xy – x + y – 3

= 4x2 + 3x2+ 3y2– 4y2– x + y – 3 + 8

= 7x2 – y2– x + y + 5.

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