分解因式:(1)a2-4ab+4b2(2)4+12(x-y)+9(x-y)2(3)16x4-1(4)(2a-b)2+8ab.
题型:解答题难度:一般来源:不详
分解因式: (1)a2-4ab+4b2 (2)4+12(x-y)+9(x-y)2 (3)16x4-1 (4)(2a-b)2+8ab. |
答案
(1)a2-4ab+4b2 =a2-2•a•2b+(2b)2 =(a-2b)2;
(2)4+12(x-y)+9(x-y)2 =22+2×2×3(x-y)+[3(x-y)]2 =[2+3(x-y)]2 =(2+3x-3y)2;
(3)16x4-1 =(4x2)2-1 =(4x2+1)(4x2-1) =(4x2+1)(2x+1)(2x-1);
(4)(2a-b)2+8ab =4a2-4ab+b2+8ab =4a2+4ab+b2 =(2a+b)2. |
举一反三
水压机内有4根相同的圆柱形空心圆钢立柱,每根的高度为h=18m,外径D=1m,内径d=0.4m,每立方米钢的质量为7.8吨,求这4根钢立柱的总质量(π取3.14,结果保留两个有效数字). |
下列分解因式正确的是( )A.x3-x=x(x2-1) | B.m2+m-6=(m+3)(m-2) | C.(a+4)(a-4)=a2-16 | D.x2+y2=(x+y)(x-y) |
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