已知A=4x2-4xy+y2,B=x2+xy-5y2,求:
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已知A=4x2-4xy+y2,B=x2+xy-5y2,求:
(1)A-3B;
(2)3A+B.
(1)A-3B;
(2)3A+B.
(1)∵A=4x2-4xy+y,2B=x2+xy-5y2,
∴A-3B=(4x2-4xy+y2)-3(x2+xy-5y2)
=4x2-4xy+y2-3x2-3xy+15y2
=(4-3)x2-(4+3)xy+(1+15)y2
=x2-7xy+16y2;
(2)∵A=4x2-4xy+y2,B=x2+xy-5y2,
∴3A+B=3(4x2-4xy+y2)+(x2+xy-5y2)
=12x2-12xy+3y2+x2+xy-5y2
=(12+1)x2-(12-1)xy+(3-5)y2
=13x2-11xy-2y2.
∴A-3B=(4x2-4xy+y2)-3(x2+xy-5y2)
=4x2-4xy+y2-3x2-3xy+15y2
=(4-3)x2-(4+3)xy+(1+15)y2
=x2-7xy+16y2;
(2)∵A=4x2-4xy+y2,B=x2+xy-5y2,
∴3A+B=3(4x2-4xy+y2)+(x2+xy-5y2)
=12x2-12xy+3y2+x2+xy-5y2
=(12+1)x2-(12-1)xy+(3-5)y2
=13x2-11xy-2y2.
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