Question

phân tích thành nhân tử

1,\(\left(x-6\right)^2-x^2+36\)

2,\(x^3+y^3+z^3-3xyz\)

3,\(\left(a-b\right)^3+\left(b-c\right)^3+\left(c+a\right)^3\)

Answer 1

1.

\((x-6)^2-x^2+36=(x-6)^2-(x^2-36)=(x-6)^2-(x-6)(x+6)\)

\(=(x-6)[x-6-(x+6)]=-12(x-6)\)

2. Sử dụng hằng đẳng thức đáng nhớ

\(x^3+y^3+z^3-3xyz=(x+y+z)^3-3(x+y)(y+z)(x+z)-3xyz\)

\(=(x+y+z)^3-3[(x+y)(y+z)(x+z)+xyz]=(x+y+z)^3-3(xy+yz+xz)(x+y+z)\)

\(=(x+y+z)[(x+y+z)^2-3(xy+yz+xz)]=(x+y+z)(x^2+y^2+z^2-xy-yz-xz)\)

3.

Áp dụng hằng đẳng thức đáng nhớ, với \((a-b,b-c,c-a)=(x,y,z)\)

\((a-b)^3+(b-c)^3+(c-a)^3=x^3+y^3+z^3\)

\(=(x+y+z)^3-3(x+y)(y+z)(z+x)\)

\(=(a-b+b-c+c-a)^3-3(a-b+b-c)(b-c+c-a)(c-a+a-b)\)

\(=-3(a-c)(b-a)(c-b)\)

Answer 2

1, \(\left(x-6\right)^2-x^2+36\)

\(=\left(x-6\right)^2-\left(x-6\right)\left(x+6\right)\)

\(=\left(x-6\right)\left(x-6-x-6\right)\)

\(=-12\left(x-6\right)\)

2, \(x^3+y^3+z^3-3xyz\)

\(=\left(x+y\right)^3+z^3-3xyz-3xy\left(x+y\right)\)

\(=\left(x+y+z\right)\left(x^2+2xy+y^2-yz-zx+z^2\right)-3xy\left(x+y+z\right)\)

\(=\left(x+y+z\right)\left(x^2+y^2+z^2-xy-yz-xz\right)\)

3, sai đề

Answer 3

2/

Answer 4

\(x^3 + y^3 + z^3 - 3xyz\)

= \((x^3 + 3x^2y + 3xy^2 +y^3) + z^3 - 3x^2y - 3xy^2 - 3xyz\)

= \((x + y)^3 + z^3 - 3xy(x + y +z)\)

= \((x + y + z)[(x+y)^2 - (x + y)z + z^2] - 3xy(x + y +z)\)

\(= (x + y + z)(x^2 + 2xy + y^2 - xz - yz + z^2 - 3xy)\)

= (x + y + z)(x^2 + y^2 + z^2 - xy - xz -yz)

Answer 5

1/

\(\left(x-6\right)^2-x^2+36=\left(x-6+x\right)\left(x-6-x\right)+36\\ =\left(2x-6\right).\left(-6\right)+\left(-6\right)^2=\left(-6\right)\left(2x-6-6\right)=\left(-6\right)\left(2x-12\right)=12\left(6-x\right)\)