Cho \(P = 6{x^2}y – 4xy + 9{x^2} – 7y + 1\) và \(Q = – 3xy – 8{y^2}x – 5y + x – 11\)
a) Tìm đa thức R, biết rằng R – Q = P.
b) Tìm đa thức M, biết rằng P + M = Q.
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\(\eqalign{ & a)R – Q = P \cr & R = P + Q \cr & R = (6{x^2}y – 4xy + 9{x^2} – 7y + 1) + ( – 3xy – 8{y^2}x – 5y + x – 11) \cr & R = 6{x^2}y – 4xy + 9{x^2} – 7y + 1 – 3xy – 8{y^2}x – 5y + x – 11 \cr & R = 6{x^2}y + ( – 4xy – 3xy) + 9{x^2} + ( – 7y – 5y) + (1 – 11) – 8{y^2}x + x \cr & R = 6{x^2}y – 7xy + 9{x^2} – 12y – 10 – 8{y^2}x + x. \cr & b)P + M = Q \cr & M = Q – P \cr & M = ( – 3xy – 8{y^2}x – 5y + x – 11) – (6{x^2}y – 4xy + 9{x^2} – 7y + 1) \cr & M = – 3xy – 8{y^2}x – 5y + x – 11 – 6{x^2}y + 4xy – 9{x^2} + 7y – 1 \cr & M = ( – 3xy + 4xy) – 8{y^2}x + ( – 5y + 7y) + x + ( – 11 – 1) – 6{x^2}y – 9{x^2} \cr & M = xy – 8{y^2}x + 2y + x – 12 – 6{x^2}y – 9{x^2}. \cr}\)