题目内容
计算:①(
1 |
2 |
1 |
2 |
1 |
2 |
②(x-3)(x+4)-(x+1)(x-2);
③8x2-(x-2)(3x+1)-2(x+1)(x-5)
④(3x+4)2-(2x+3)(2x-3)
⑤-6xy(x2-2xy-y2)-3xy(2x2-4xy+y2)
⑥(2x-y-1)(2x+y-1)
分析:只需利用完全平方公式以及单项式乘以多项式、多项式乘以多项式的方法,对所求代数式进行化简即可.
解答:解:①(
m+2)2-(2-
m)(-2-
m),
=
m2+4+2m-(-4-m+m+
m2),
=2m+8;
②(x-3)(x+4)-(x+1)(x-2),
=(x2+4x-3x-12)-(x2-2x+x-2),
=2x-10;
③8x2-(x-2)(3x+1)-2(x+1)(x-5),
=8x2-(3x2+x-6x-2)-2(x2-5x+x-5),
=3x2+13x+12;
④(3x+4)2-(2x+3)(2x-3),
=(9x2+16+24x)-(4x2-6x+6x-9),
=5x2+24x+25,
⑤-6xy(x2-2xy-y2)-3xy(2x2-4xy+y2)
=-12x3y+24x2y2+3xy3;
⑥(2x-y-1)(2x+y-1),
=4x2-4x+1-y2.
1 |
2 |
1 |
2 |
1 |
2 |
=
1 |
4 |
1 |
4 |
=2m+8;
②(x-3)(x+4)-(x+1)(x-2),
=(x2+4x-3x-12)-(x2-2x+x-2),
=2x-10;
③8x2-(x-2)(3x+1)-2(x+1)(x-5),
=8x2-(3x2+x-6x-2)-2(x2-5x+x-5),
=3x2+13x+12;
④(3x+4)2-(2x+3)(2x-3),
=(9x2+16+24x)-(4x2-6x+6x-9),
=5x2+24x+25,
⑤-6xy(x2-2xy-y2)-3xy(2x2-4xy+y2)
=-12x3y+24x2y2+3xy3;
⑥(2x-y-1)(2x+y-1),
=4x2-4x+1-y2.
点评:本题考查了完全平方公式、单项式乘以多项式、多项式乘以多项式等考点,要注意掌握.
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①(-
)2=
;②
=x+y;③
=
;④
÷
=
.
①(-
a3 |
b4 |
a6 |
b2 |
x2+y2 |
x+y |
a |
2b |
ac |
2bc |
3m |
2n |
3m2 |
n |
1 |
2m |
A、①②③④ | B、②③④ |
C、③④ | D、④ |