x3+x2-4x-4 分解因式
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x3+x2-4x-4 分解因式
x^3+x^2-4x-4
=x^2(x+1)-4(x+1)
=(x^2-4)(x+1)
=(x-2)(x+2)(x+1)
再问: 5x2+6y-15x-2xy ax2+3x2-4a-12 a2+x2-bx-ab+2ax x4-zx2+x2y-y+1 a2(a+1)-b2(b+1) ab(a2+b2)+cbca2+b2
再答: 5x2+6y-15x-2xy =5x^2-15x-2xy+6y =5x(x-3)-2y(x-3) =(5x-2y)(x-3) ax^2+3x^2-4a-12 =ax^2-4a+3x^2-12 =a(x^2-4)+3(x^2-4) =(a+3)(x^2-4) =(a+3)(x-2)(x+2) a2+x2-bx-ab+2ax =a^2+2ax+x^2-bx-ab =(a+x)^2-b(x+a) =(a+x)[(x+a)-b] =(a+x)(x+a-b) x^4-2x^2+x^2y-y+1 =x^4-2x^2+1+x^2y-y =(x^2-1)^2+y(x^2-1) =(x^2-1)[(x^2-1)+y] =(x+1)(x-1)(x^2-1+y) a^2(a+1)-b^2(b+1) =a^3+a^2-b^3-b^2 =(a^3-b^3)+(a^2-b^2) =(a-b)(a^2+ab+b^2)+(a-b)(a+b) =(a-b)(a^2+ab+b^2+a+b) ab(a^2+b^2)+cb(a^2+b^2) =b(a^2+b^2)(a+c)
=x^2(x+1)-4(x+1)
=(x^2-4)(x+1)
=(x-2)(x+2)(x+1)
再问: 5x2+6y-15x-2xy ax2+3x2-4a-12 a2+x2-bx-ab+2ax x4-zx2+x2y-y+1 a2(a+1)-b2(b+1) ab(a2+b2)+cbca2+b2
再答: 5x2+6y-15x-2xy =5x^2-15x-2xy+6y =5x(x-3)-2y(x-3) =(5x-2y)(x-3) ax^2+3x^2-4a-12 =ax^2-4a+3x^2-12 =a(x^2-4)+3(x^2-4) =(a+3)(x^2-4) =(a+3)(x-2)(x+2) a2+x2-bx-ab+2ax =a^2+2ax+x^2-bx-ab =(a+x)^2-b(x+a) =(a+x)[(x+a)-b] =(a+x)(x+a-b) x^4-2x^2+x^2y-y+1 =x^4-2x^2+1+x^2y-y =(x^2-1)^2+y(x^2-1) =(x^2-1)[(x^2-1)+y] =(x+1)(x-1)(x^2-1+y) a^2(a+1)-b^2(b+1) =a^3+a^2-b^3-b^2 =(a^3-b^3)+(a^2-b^2) =(a-b)(a^2+ab+b^2)+(a-b)(a+b) =(a-b)(a^2+ab+b^2+a+b) ab(a^2+b^2)+cb(a^2+b^2) =b(a^2+b^2)(a+c)
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