Question

phân tích đa thức thành nhân tử :

a ) a^3 x ( b - c ) + b^3 x ( c - a ) + c^3 x ( a - b )

b ) ( a + b ) x ( a^2 - b^2 ) + ( b + c ) x ( b^2 - c^2 ) + ( c + a ) x ( c^2 - a^2 )

Answer 1

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

\(D=a^3\left(b-c\right)+\left[b^3\left(c-a\right)+c^3\left(a-b\right)\right]\)

\(D=a^3\left(b-c\right)\left(b^3c-ab^3+ac^3-bc^3\right)\)

\(D=a^3\left(b-c\right)\left[\left(b^3c-bc^3\right)-\left(ab^3-ac^3\right)\right]\)

\(D=a^3\left(b-c\right)\left[bc\left(b^2-c^2\right)-a\left(b^3-c^3\right)\right]\)

\(D=a^3\left(b-c\right)\left[bc\left(b-c\right)\left(b+c\right)-a\left(b-c\right)\left(b^2+bc+c^2\right)\right]\)

\(D=\left(b-c\right)\left[a^3+bc\left(b+c\right)-a\left(b^2+bc+c^2\right)\right]\)

\(D=\left(b-c\right)\left(a^3+b^2c+bc^2-ab^2-abc-ac^2\right)\)

\(D=\left(b-c\right)\left[\left(b^2c-ab^2\right)+\left(bc^2-abc\right)-\left(ac^2-a^3\right)\right]\)

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

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

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

\(D=\left(b-c\right)\left(c-a\right)\left(b^2+bc-ac-a^2\right)\)

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

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

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

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

Chúc bạn học tốt.