Question

Phân tích đa thức thành nhân tử :

1. ab(a-b) + b(b-c) - ac(a-c)

2. (1+x^2)^2+4x^3-4x

3. a(a^2-7)-6

4. x^4+4x^2-5

5. (9x^2)^2+4

Answer 1

1.

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

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

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

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

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

2.

\((1+x^2)^2+4x^3-4x\)

\(=x^4+2x^2+1+4x^3-4x\)

\(=x^4-2x^2+1+4x^3-4x+4x^2\)

\(=(x^2-1)^2+4x(x^2-1)+4x^2\)

\(=(x^2-1+2x)^2\)

3.

\(a(a^2-7)-6=a^3-7a-6=a^3-a-(6a+6)\)

\(=a(a^2-1)-6(a+1)=a(a-1)(a+1)-6(a+1)\)

\(=(a+1)(a^2-a-6)=(a+1)(a^2-3a+2a-6)\)

\(=(a+1)[a(a-3)+2(a-3)]=(a+1)(a-3)(a+2)\)

Answer 2

4.

\(x^4+4x^2-5=x^4-x^2+5x^2-5\)

\(=x^2(x^2-1)+5(x^2-1)=(x^2+5)(x^2-1)=(x^2+5)(x-1)(x+1)\)

5.

\((9x^2)^2+4=(9x^2)^2+2.9x^2.2+2^2-36x^2\)

\(=(9x^2+2)^2-(6x)^2=(9x^2+2-6x)(9x^2+2+6x)\)