因式分解30题(要过程)am+an+bm+bnx^2+5y-xy-5xx2+xy+2xz+x(a+b)x-(b+a)y-12x(x-y)-(y-x)x^22x^2+4x+2x(x+z)-y(y+z)2(x^2-3ab)+x(4a-3b)4x^2+12xy+9y^2-25x^4-1616x^4-1x^2+9x+8x^2-10xy+24y^22x^2+15xy-8y^23x^2-6xy+3y^224x^2+22x-21-x^2+4xy-

Question

因式分解30题(要过程)
am+an+bm+bn x^2+5y-xy-5x x2+xy+2xz+x (a+b)x-(b+a)y -12x(x-y)-(y-x)x^2 2x^2+4x+2 x(x+z)-y(y+z) 2(x^2-3ab)+x(4a-3b) 4x^2+12xy+9y^2-25 x^4-16 16x^4-1 x^2+9x+8 x^2-10xy+24y^2 2x^2+15xy-8y^2 3x^2-6xy+3y^2 24x^2+22x-21 -x^2+4xy-4y^2 8xy+x^2y^2+12 m^3-m^2-20m 36x^2-96xy+64y^2 81x^2+18xy+y^2 n+10nt+25nt^2 25分之9乘以x^2+2分之3乘以xy+16分之25乘以y^2 (a-b)^3+2ab(b-a) -12x^3y^3z^3-18x^3y^2z^4+24x^2y^4z^3-6x^2y^3z^4 x^3-x^2+4分之1乘以x (a-b)^2(a-b)(a-c)+(a-b)(b+C) (x+y)^2-14x(x+y)+49x^2 (x^2+x+1)^2+2(x^2+x+1)(x^2+x-1)+(x^2+x-1)^2

Answer 1

am+an+bm+bn=a(m+n)+b(m+n)=(m+n)(a+b) x^2+5y-xy-5x=x(x-5)-y(x-5)=(x-5)(x-y) x2+xy+2xz+x=x(x+y+2z+1) (a+b)x-(b+a)y=(a+b)(x-y) -12x(x-y)-(y-x)x^2=(y-x)(12x-x^2)=x(y-x)(12-x) 2x^2+4x+2=2(x^2+2x+1)=2(x+1)^2 x(x+z)-y(y+z)=x^2+xz-y^2-yz=(x+y)(x-y)+z(x-y)=(x-y)(x+y+z) 2(x^2-3ab)+x(4a-3b)=2x^2-6ab+4ax-3bx=2x(x+2a)-3b(x+2a)=(x+2a)(2x-3b) 4x^2+12xy+9y^2-25=(2x-3y)^2-5^2=(2x-3y-5)(2x-3y+5) x^4-16=(x-2)(x+2)(x^2+4) 16x^4-1=(2x-1)(2x+1)(2x^2+1) x^2+9x+8=(x+1)(x+8) x^2-10xy+24y^2=(x-4y)(x-6y) 2x^2+15xy-8y^2=(2x-y)(x+8y) 3x^2-6xy+3y^2=3(x-y)^2 24x^2+22x-21=(2x+3)(12x-7) -x^2+4xy-4y^2=-(x-2y)^2 8xy+x^2y^2+12=(xy+2)(xy+6) m^3-m^2-20m=m(m+4)(m-5) 36x^2-96xy+64y^2=(6x-8y)^2=4(3x-4y)^2 81x^2+18xy+y^2=(9x+y)^2 n+10nt+25nt^2=n(5t+1)^2 25分之9乘以x^2+2分之3乘以xy+16分之25乘以y^2=(3x/5+5y/4)^2 (a-b)^3+2ab(b-a)=(a-b)(a^2-2ab+b^2+2ab)=(a-b)(a^2+b^2) -12x^3y^3z^3-18x^3y^2z^4+24x^2y^4z^3-6x^2y^3z^4=-6x^2y^2z^2(2xy+3xz^2-4y^2z+1) x^3-x^2+4分之1乘以x=x(x-1/2)^2 (a-b)^2(a-b)(a-c)+(a-b)(b+C)=(a-b)[(a-b)^2(a-c)+(b+c)] (x+y)^2-14x(x+y)+49x^2=(x+y+7x)^2=(8x+y)^2 (x^2+x+1)^2+2(x^2+x+1)(x^2+x-1)+(x^2+x-1)^2=(x^2+x+1+x^2+x-1)^2=4x^2(x+1)^2