怎样作整式的加减法
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怎样作整式的加减法
答:整式加减的一般步骤是:
(1)如果遇到括号,按去括号法则先去括号;
(2)合并同类项.
[例1] 求多项式12x2+8x-5与19x2-17x-23的和与差.
解:(12x2+8x-5)+(19x2-17x-23)
=12x2+8x-5+19x2-17x-23
=31x2-9x-28(12x2+8x-5)-(19x2-17x-23)
=12x2+8x-5-19x2+17x+23
=-7x2+25x+18
[例2] 计算:2a2-3b2-[3(a2-4b-1)-2(b+8a2-15)+24a2-(8a-7b)]-(b2-10a).
解:2a2-3b2-[3(a2-4b-1)-2(b+8a2-15)+24a2-(8a-7b)]-(b2-10a)
=2a2-3b2-[3a2-12b-3-2b-16a2+30+24a2-8a+7b]-b2+10a
=2a2-3b2-[11a2-8a-7b+27]-b2+10a
=2a2-3b2-11a2+8a+7b-27-b2+10a
=-9a2-4b2+18a+7b-27
[例3] 设A=5x3-2x2y+xy2-xy,B=4x3+10x2y-6xy2+9xy,C=16x2y-17xy2-15y3-14xy.求:(1)2A-(B-C) (2)A+3B-2C
解:(1)2A=2(5x3-2x2y+xy2-xy)
=10x3-4x2y+2xy2-2xy
B-C=(4x3+10x2y-6xy2+9xy)-(16x2y-17xy2-15y3-14xy)
=4x3+10x2y-6xy2+9xy-16x2y+17xy2+15y3+14xy
=4x3-6x2y+11xy2+23xy+15y3
∴2A-(B-C)=(10x3-4x2y+2xy2-2xy)-(4x3-
6x2y+11xy2+23xy+15y3)
=10x3-4x2y+2xy2-2xy-4x3+6x2y-11xy2-23xy-15y3
=6x3+2x2y-9xy2-25xy-15y3
(2)3B=3(4x3+10x2y-6xy2+9xy)
=12x3+30x2y-18xy2+27xy
2C=2(16x2y-17xy2-15y3-14xy)
=32x2y-34xy2-30y3-28xy
∴A+3B=2C=(5x3-2x2y+xy2-xy)+(12x3+30x2y-18xy2+27xy)-(32x2y-34xy2-30y3-28xy) =17x3-4x2y+17xy2+54xy+30y3
[例4] 化简求值:
解:3x2y-[2x2y-(2xyz-x2z)-4x2z]-xyz-(x2y+3x2z)
=3x2y-[2x2y-2xyz+x2z-4x2z]-xyz-x2y-3x2z
=3x2y-(2x2y-2xyz-3x2z)-xyz-x2y-3x2z.
=3x2y-2x2y+2xyz+3x2z-xyz-x2y-3x2z
=xyz