Question

因式分解 x的4次方-6x的3次方+9x的2次方-16还有下面的

2x的3次方-x的2次方-2x+1
9x的4次方-25x的2次方y的2次方+16y的4次方
6（a-b）的2次方+13（a-b）+5
3a的2次方-6ab+3b的2次方-5a+5b
m的4次方+2m的3次方n-2m n的3次方-n的4次方
x的3次方-3x+2
xy+（x+1）（y+1）（xy+1）

Answer 1

1. x^4-6*x^3+9*x^2-16=X^2*(x-3)^2-16

2. 2*x^3-x^2-2x+1=2*x^3-(x+1)^2+2

3. 9*x^4-25*X^2*y^2+16*y^4=(x^2-*y^2)(9*x^2-16y^2)=(x+y)(x-y)(9*x^2-16*y^2)

4. 6*(a-b)^2+13(a-b)+5=(2*(a-b)+1)*(3*(a-b)+5)

5. 3*a^2-6ab+3*b^2-5a+5b=3*(a-b)^2-5(a-b)=(a-b)(3(a-b)-5)

6. m^4+2*m^3*n-2m*n^3-n^4=m^4+2mn(m^2-n^2)-n^4=(m^2+n^2)(m^2-n^2)+2mn(m^2-n^2)=(m+n)^2*(m+n)(m-n)=(m+n)^3(m-n)

7. x^3-3x+2=x^3-x^2+(x-1)(x-2)=x^2(x-1)+(x-1)(x-2)=(x-1)(x^2+x-2)

8. xy+(x+1)(y+1)(xy+1)=(xy+1)(1+(x+1)(y+1))-1

Answer 2

x^4-6x^3+9x^2-16=(x²-3x)²-16=(x²-3x+4)(x²-3x-4)=(x²-3x+4)(x+1)(x-4)
2x^3-x^2-2x+1=x²(2x-1)-(2x-1)=(2x-1)(x²-1)=(2x-1)(x+1)(x-1)

9x^4-25x^2y^2+16y^4=(9x²-16y²)(x²-y²)=(3x+4y)(3x-4y)(x+y)(x-y)

6(a-b)^2+13(a-b)+5=[2(a-b)+1][3(a-b)+5]=(2a-2b+1)(3a-3b+5)

3a^2-6ab+3b^2-5a+5b=3(a-b)²-5(a-b)=(a-b)(3a-3b-5)

m^4+2m^3n-2mn^3-n^4=(m²+n²)(m²-n²)+2mn(m²-n²)=(m²-n²)(m+n)²

x^3-3x+2=x^3-x-2x+2=x(x+1)(x-1)-2(x-1)=(x-1)(x²+x-2)=(x-1)²(x+2)

xy+(x+1)(y+1)(xy+1)=xy+(xy+x+y+1)(xy+1)=xy+(xy+1)²+(x+y)(xy+1)

=(xy+x+1)(xy+y+1)

Answer 3

4