Question

phân tích các đa thức sau thành nhân tử:

1/(1+x^2)^2-4x(1-x^2)

2/(x^2-8)^2+36

3/x^4+4

4/x^4+64

5/64x^4+1

6/81x^4+4

7/4x^4+81

8/64x^4+y^4

9/x^4+4y^4

10/x^4+x^2+1

Answer 1

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

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

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

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

2: \(\left(x^2-8\right)^2+36\)

\(=x^4-16x^2+64+36\)

\(=x^4-16x^2+100\)

\(=x^4+20x^2+100-36x^2\)

\(=\left(x^2+10\right)^2-\left(6x\right)^2\)

\(=\left(x^2+6x+10\right)\left(x^2-6x+10\right)\)

3: \(x^4+4=x^4+4x^2+4-4x^2\)

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

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

4: \(x^4+64=x^4+16x^2+64-16x^2\)

\(=\left(x^2+8\right)^2-16x^2\)

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

5: \(64x^4+1=64x^4+16x^2+1-16x^2\)

\(=\left(8x^2+1\right)^2-16x^2\)

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