Question

phân tích đa thức sau thành nhân tử

a) x⁴-5x²+4

b) (x+y+z)³-x³-y³-z³

Answer 1

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)

Answer 2

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

Answer 3

a, x^4 - 5x^2 + 4

= x^4 - 4x^2- x+ 4

= x^2  . (x^2 - 4) - (x^2 - 4)

= (x^2 - 4) . (x^2 - 1)

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

Answer 4

a, x^4 - 5x^2 + 4

= x^4 - 4x^2- x+ 4

= x^2  . (x^2 - 4) - (x^2 - 4)

= (x^2 - 4) . (x^2 - 1)

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

Answer 5

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

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

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

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

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