Question

phân tích đa thức thành nhân tử

a, \(ab\left(a+b\right)-bc\left(b+c\right)+ac\left(a-c\right)\)

b, \(\left(a+b\right)\left(a^2-b^2\right)+\left(b+c\right)\left(b^2-c^2\right)+\left(c+a\right)\left(c^2-a^2\right)\)

c, \(a^3\left(c-b^2\right)+b^3\left(a-c^2\right)+c^3\left(b-a^2\right)+abc\left(abc-1\right)\)

Answer 1

a)= ab (a + b) - bc [( a + b) - (a - c)] + ac (a - c)

= ab (a + b) - bc (a + b) + bc (a - c) +ac (a - c)

= b (a + b) (a - c) + c (a - c) (a + b)

= (a + b) (a - c) (b + c)

Answer 2

b) \(=\left(a+b\right)\left(a^2-b^2\right)-\left(b+c\right)\left[\left(a^2-b^2\right)+\left(c^2-a^2\right)\right]+\left(c+a\right)\left(c^2-a^2\right)\)

\(=\left(a^2-b^2\right)\left[\left(a+b\right)-\left(b+c\right)\right]+\left(c^2-a^2\right)\left[\left(c+a\right)-\left(b+c\right)\right]\)

\(=\left(a-b\right)\left(a+b\right)\left(a-c\right)-\left(a-c\right)\left(a+c\right)\left(a-b\right)\)

\(=\left(a-b\right)\left(a-c\right)\left[\left(a+b\right)-\left(a+c\right)\right]\)

\(=\left(a-b\right)\left(a-c\right)\left(b-c\right)\)