七年级因式分解计算题及答案100道(七年级因式分解计算题及答案)

导读 你可真狠 要这么多题目1. 5ax+5bx+3ay+3by 解法:=5x(a+b)+3y(a+b) =(5x+3y)(a+b) 2. x^3-x^2+x-1 解法:=(x^3-x^2)+(x-1)...

你可真狠 要这么多题目1. 5ax+5bx+3ay+3by 解法:=5x(a+b)+3y(a+b) =(5x+3y)(a+b) 2. x^3-x^2+x-1 解法:=(x^3-x^2)+(x-1) =x^2(x-1)+ (x-1) =(x-1)(x^2+1) 3. x2-x-y2-y 解法:=(x2-y2)-(x+y) =(x+y)(x-y)-(x+y) =(x+y)(x-y-1)bc(b+c)+ca(c-a)-ab(a+b) =bc(c-a+a+b)+ca(c-a)-ab(a+b) =bc(c-a)+bc(a+b)+ca(c-a)-ab(a+b) =bc(c-a)+ca(c-a)+bc(a+b)-ab(a+b) =(bc+ca)(c-a)+(bc-ab)(a+b) =c(c-a)(b+a)+b(a+b)(c-a) =(c+b)(c-a)(a+b).x^2+3x-40 =x^2+3x+2.25-42.25 =(x+1.5)^2-(6.5)^2 =(x+8)(x-5).(x^2+x+1)(x^2+x+2)-12时。

可以令y=x^2+x,则 原式=(y+1)(y+2)-12 =y^2+3y+2-12=y^2+3y-10 =(y+5)(y-2) =(x^2+x+5)(x^2+x-2) =(x^2+x+5)(x+2)(x-1).(1+y)^2-2x^2(1+y^2)+x^4(1-y)^2 解:原式=(1+y)^2+2(1+y)x^2(1+y)+x^4(1-y)^2-2(1+y)x^2(1-y)-2x^2(1+y^2) =[(1+y)+x^2(1-y)]^2-2(1+y)x^2(1-y)-2x^2(1+y^2) =[(1+y)+x^2(1-y)]^2-(2x)^2 =[(1+y)+x^2(1-y)+2x]·[(1+y)+x^2(1-y)-2x] =(x^2-x^2y+2x+y+1)(x^2-x^2y-2x+y+1) =[(x+1)^2-y(x^2-1)][(x-1)^2-y(x^2-1)] =(x+1)(x+1-xy+y)(x-1)(x-1-xy-y) x^5+3x^4y-5x^3y^2+4xy^4+12y^5 解:原式=(x^5+3x^4y)-(5x^3y^2+15x^2y^3)+(4xy^4+12y^5) =x^4(x+3y)-5x^2y^2(x+3y)+4y^4(x+3y) =(x+3y)(x^4-5x^2y^2+4y^4) =(x+3y)(x^2-4y^2)(x^2-y^2) =(x+3y)(x+y)(x-y)(x+2y)(x-2y) 分解因式m +5n-mn-5m 解:m +5n-mn-5m= m -5m -mn+5n = (m -5m )+(-mn+5n) =m(m-5)-n(m-5) =(m-5)(m-n) 分解因式bc(b+c)+ca(c-a)-ab(a+b) 解:bc(b+c)+ca(c-a)-ab(a+b)=bc(c-a+a+b)+ca(c-a)-ab(a+b) =bc(c-a)+ca(c-a)+bc(a+b)-ab(a+b) =c(c-a)(b+a)+b(a+b)(c-a) =(c+b)(c-a)(a+b) 1.(2a-b)²+8ab2.y²-2y-x²+13.x²-xy+yz-xz4.6x²+5x-45.2a²-7ab+6b²6.(x²-2x)²+2(x²-2x)+17.(x²-2x)²-14(x²-2x)-15 8.x²(x-y)+(y-x)9.169(a+b)²-121(a-b)²10.(x-3)(x-5)+1 答案:1.(2a-b)²+8ab=(2a+b)²2.y²-2y-x²+1=(y-1)²-x²=(y-1-x)(y-1+x)3.x²-xy+yz-xz =x(x-y)-z(x-y)=(x-z)(x-y)4.6x²+5x-4 =(2x-1)(3x+4)5.2a²-7ab+6b²=(2a-3b)(a-2b)6.(x²-2x)²+2(x²-2x)+1 =(x²-2x+1)²=(x-1)^47.(x²-2x)²-14(x²-2x)-15 =(x²-2x-15)(x²-2x+1)=(x+3)(x-5)(x-1)² 8.x²(x-y)+(y-x) =(x²-1)(x-y)=(x+1)(x-1)(x-y)9.169(a+b)²-121(a-b)² =(14a+14b-11a+11b)(14a+14b+11a-11b) =(3a+25b)(25a+3b)10.(x-3)(x-5)+1 =(x-3)²-2(x-3)+1 =(x-3-1)²=(x-4)² -5a^2+16a=a(16-5a)8x^2-4x=4x(2x-1)15p+10p^2=5p(3+2p)-3x^2y-6xy=-3xy(x+2y)14m^3n^2-6m^2n^3=2m^2n^2(7m-6n)27a^2 b^3 c+18ab^2=9ab^2(3abc+2)18xy^2 z^3+12x^2 y^2=6xy^2(3z^3+2x)8m^2 n^2 -6m^3 n^2=2m^2 n^2(4-3m)因式分解3a3b2c-6a2b2c2+9ab2c3=3ab^2 c(a^2-2ac+3c^2) 3.因式分解xy+6-2x-3y=(x-3)(y-2) 4.因式分解x2(x-y)+y2(y-x)=(x+y)(x-y)^2 5.因式分解2x2-(a-2b)x-ab=(2x-a)(x+b) 6.因式分解a4-9a2b2=a^2(a+3b)(a-3b) 7.若已知x3+3x2-4含有x-1的因式。

试分解x3+3x2-4=(x-1)(x+2)^2 8.因式分解ab(x2-y2)+xy(a2-b2)=(ay+bx)(ax-by) 9.因式分解(x+y)(a-b-c)+(x-y)(b+c-a)=2y(a-b-c) 10.因式分解a2-a-b2-b=(a+b)(a-b-1) 11.因式分解(3a-b)2-4(3a-b)(a+3b)+4(a+3b)2=[3a-b-2(a+3b)]^2=(a-7b)^2 12.因式分解(a+3)2-6(a+3)=(a+3)(a-3) 13.因式分解(x+1)2(x+2)-(x+1)(x+2)2=-(x+1)(x+2) abc+ab-4a=a(bc+b-4) (2)16x2-81=(4x+9)(4x-9) (3)9x2-30x+25=(3x-5)^2 (4)x2-7x-30=(x-10)(x+3) 35.因式分解x2-25=(x+5)(x-5) 36.因式分解x2-20x+100=(x-10)^2 37.因式分解x2+4x+3=(x+1)(x+3) 38.因式分解4x2-12x+5=(2x-1)(2x-5) 39.因式分解下列各式: (1)3ax2-6ax=3ax(x-2) (2)x(x+2)-x=x(x+1) (3)x2-4x-ax+4a=(x-4)(x-a) (4)25x2-49=(5x-9)(5x+9) (5)36x2-60x+25=(6x-5)^2 (6)4x2+12x+9=(2x+3)^2 (7)x2-9x+18=(x-3)(x-6) (8)2x2-5x-3=(x-3)(2x+1) (9)12x2-50x+8=2(6x-1)(x-4) 40.因式分解(x+2)(x-3)+(x+2)(x+4)=(x+2)(2x-1) 41.因式分解2ax2-3x+2ax-3= (x+1)(2ax-3) 42.因式分解9x2-66x+121=(3x-11)^2 43.因式分解8-2x2=2(2+x)(2-x) 44.因式分解x2-x+14 =整数内无法分解 45.因式分解9x2-30x+25=(3x-5)^2 46.因式分解-20x2+9x+20=(-4x+5)(5x+4) 47.因式分解12x2-29x+15=(4x-3)(3x-5) 48.因式分解36x2+39x+9=3(3x+1)(4x+3) 49.因式分解21x2-31x-22=(21x+11)(x-2) 50.因式分解9x4-35x2-4=(9x^2+1)(x+2)(x-2) 51.因式分解(2x+1)(x+1)+(2x+1)(x-3)=2(x-1)(2x+1) 52.因式分解2ax2-3x+2ax-3=(x+1)(2ax-3) 53.因式分解x(y+2)-x-y-1=(x-1)(y+1) 54.因式分解(x2-3x)+(x-3)2=(x-3)(2x-3) 55.因式分解9x2-66x+121=(3x-11)^2 56.因式分解8-2x2=2(2-x)(2+x) 57.因式分解x4-1=(x-1)(x+1)(x^2+1) 58.因式分解x2+4x-xy-2y+4=(x+2)(x-y+2) 59.因式分解4x2-12x+5=(2x-1)(2x-5) 60.因式分解21x2-31x-22=(21x+11)(x-2) 61.因式分解4x2+4xy+y2-4x-2y-3=(2x+y-3)(2x+y+1) 62.因式分解9x5-35x3-4x=x(9x^2+1)(x+2)(x-2)。

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