sửa đề:\(\left(x+y+z\right)^3-x^3-y^3-z^3\)

giải:

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

b,W = \(x^4+x^2+1+2009x^2+2009x+2009\)

\(=\left(x^4+2x^2+1\right)-x^2+2009\left(x^2+x+1\right)\)

\(=\left(x^2+1\right)^2-x^2+2009\left(x^2+x+1\right)\)

\(=\left(x^2+1-x\right)\left(x^2+1+x\right)+2009\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left(x^2-x+2010\right)\)

a, x⁴ - 5x² + 4

= x⁴ - 4x² - x² + 4

= x² . (x² - 4) - (x² - 4)

= (x² - 4) . (x² - 1)

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

a)x⁴-5x²+4=x⁴-x²-4x²+4
                   =(x⁴-x²)-(4x^2-4)
                   =x²(x²-1)-4(x²-1)
                    =(x²-1)(x²-4)

a) \([(x-y)3 + (y-z)3]+ (z-x)3\)=\(\left(x-y+y-z\right)\left[\left(x-y\right)^2-\left(x-y\right)\left(y-z\right)+\left(y-z\right)^2\right]-\left(x-z\right)^3\)

\(=\left(x-z\right)\left[\left(\left(x-y\right)^2-\left(x-y\right)\left(y-z\right)+\left(y-z\right)^2-\left(x-z\right)^2\right)\right]\)

\(=\left(x-z\right)\left[\left(x-y\right)\left(x-y-y+z\right)+\left(y-z-x+z\right)\left(y-z+x-z\right)\right]=\left(x-z\right)\left[\left(x-2y+z\right)\left(x+z\right)-\left(x-y\right)\left(x+y-2z\right)\right]\)

\(=\left(x-z\right)\left(x-y\right)\left(x-2y+z-x-y+2z\right)=\left(x-z\right)\left(x-y\right)\left(z-y\right)3\)

b) \(=y^2\left(x^2y-x^3+z^3-z^2y\right)-z^2x^2\left(z-x\right)=y^2\left[-y\left(z^2-x^2\right)-\left(z^3-x^3\right)\right]-z^2x^2\left(z-x\right)\)

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

đến đây coi như là thành nhân tử rồi nha. em muốn gọn thì ráng ngồi nghĩ rồi tách nha. chỉ cần nhóm mấy cái có ngoặc giống nhau là đc. k khó đâu. chịu khó nghĩ để rèn luyện nha

c) \(x^8+2x^4+1-x^4=\left(x^4+1\right)^2-x^4=\left(x^4+1-x^2\right)\left(x^4+1+x^2\right)\)

\(\left(9a^3-6a^2\right)+\left(6a^2-4a\right)+\left(-9a+6\right)=3a^2\left(3a-2\right)+2a\left(3a-2\right)-3\left(3a-2\right)=\left(3a-2\right)\left(3a^2+2a-3\right)\)

d) em sửa đề đi. đề sai rồi. đồng nhất hệ số phải có dấu bằng nha.

có gì liên hệ chị. đúng nha ;)

\(a\text{)}\left(x+y+z\right)^3-x^3-y^3-z^3\)

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

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

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

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

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

\(=3\left(y+z\right)\left(x+y\right)\left(x+z\right)\)

\(b\text{)}x^4+2012x^2+2011x+2012\)

\(=\left(x^4-x\right)+\left(2012x^2+2012x+2012\right)\)

\(=x\left(x^3-1\right)+2012\left(x^2+x+1\right)\)

\(=x\left(x-1\right)\left(x^2+x+1\right)+2012\left(x^2+x+1\right)\)

\(=\left(x^2-x\right)\left(x^2+x+1\right)+2012\left(x^2+x+1\right)\)

\(=\left(x^2-x+2012\right)\left(x^2+x+1\right)\)