Question

因式分解（分组分解）

1.（2x^3-4）+（x^2-8x）
2.x^3-x^2-x+1
3.4m^2-x^2-9-6x
4.（x^2-y^2）+（6y-9）
5.a^2+2ab+b^2-2a-2b+1

Answer 1

1.（2x^3-4）+（x^2-8x）
=2x^3+x^2-8x-4
=x^2(2x+1)-4(2x+1)
=(2x+1)(x^2-4)
=(2x+1)(x-2)(x+2)

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

3.4m^2-x^2-9-6x
=4m^2-(x^2+6x+9)
=4m^2-(x+3)^2
=(2m+x+3)(2m-x-3)

4.（x^2-y^2）+（6y-9）
=x^2-y^2+6y-9
=x^2-(y^2-6y+9)
=x^2-(y-3)^2
=(x+y-3)(x-y+3)

5.a^2+2ab+b^2-2a-2b+1
=(a+b)^2-2(a+b)+1
=(a+b-1)^2

Answer 2

1：（2x^3-4）+（x^2-8x）
=2x^3-4+x^2-8x
=2x^3-8x+x^2-4
=2x(x^2-4)+(x^2-4)
=(2x+1)(x^2-4)
=(2x+1)(x+2)(x-2)
2:x^3-x^2-x+1
=x^2(x-1)-(x-1)
=(x^2-1)(x-1)
=(x+1)(x-1)(x-1)
=(x+1)(x-1)^2
3:4m^2-x^2-9-6x
=4m^2-(x^2+9+6x)
=4m^2-(x+3)^2
=(2m+x+3)(2m-x-3)
4:(x^2-y^2)+(6y-9)
=x^2-(y^2-6y+9)
=x^2-(y-3)^2
=(x+y-3)(x-y+3)
5:a^2+2ab+b^2-2a-2b+1
=(a+b)^2-2(a+b)+1
=(a+b-1)^2

Answer 3

1.（2x^3-4）+（x^2-8x）
=x^2(2x+1)-4(2x+1)
=(2x+1)(x^2-4)
=(2x+1)(x+2)(x-2)

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

3.4m^2-x^2-9-6x
=4m^2-(x+3)^2
=(2m+x+3)(2m-x-3)

4.（x^2-y^2）+（6y-9）
=x^2-(y-3)^2
=(x+y-3)(x-y+3)

5.a^2+2ab+b^2-2a-2b+1
=(a+b)^2-2(a+b)+1
=(a+b-1)^2

Answer 4

(2x^3-4）+（x^2-8x）=2X^3-8X+X^2-4=2X(X^2-4)+(X^2-4)=(2X+1)(X+2)(X-2)
x^3-x^2-x+1=(X^3-X)-(X^2-1)=X(X^2-1)-(X^2-1)=(X+1)(X-1)^2
4m^2-x^2-9-6x=4m^2-(x^2+6x+9)=4m^2-(x+3)^2=(2m+x+3)(2m-x-3)
（x^2-y^2）+（6y-9）=x^2-(y^2-6y+9)=x^2-(y-3)^2=(x+y-3)(x-y+3)
a^2+2ab+b^2-2a-2b+1=(a+b)^2-2(a+b)+1=(a+b-1)^2