因式分解x^4+x^3+x^2+x1) x^4+x^3+x^2+x 2) (ab+1)^2-(a+b)^2 3) m^2×n^2/9+2m(n^3)/3+n^4 4) x^4-7x^2+81 5) x^2+2x-y^2+6y-8
问题描述:
因式分解x^4+x^3+x^2+x
1) x^4+x^3+x^2+x 2) (ab+1)^2-(a+b)^2 3) m^2×n^2/9+2m(n^3)/3+n^4 4) x^4-7x^2+81 5) x^2+2x-y^2+6y-8
答
1) x^4+x^3+x^2+x =(x4+x)+(x+x) =x(x+1)+x(x+1) =x(x+1)(x+1) 2) (ab+1)^2-(a+b)^2 =(ab+a+b+1)(ab-a-b+1) =(a+1)(b+1)(a-1)(b-1) 3) m^2×n^2/9+2m(n^3)/3+n^4 =n(m/ 9 +2mn/3+n) =n(m/3+n) 4) x^4-7x^2+81 =(x^4+18x+81)- 25x =(x+5x+9)(x-5x+9) 5) x^2+2x-y^2+6y-8 =(x+2x+1)-(y-6y+9) =(x+1) - (y-3) =(x+y-2)(x-y+4)