Bài 6:
b: \(x^4+64\)
\(=x^4+16x^2+64-16x^2\)
\(=\left(x^2+8\right)^2-\left(4x\right)^2=\left(x^2+8+4x\right)\left(x^2+8-4x\right)\)
c: \(x^4+4y^4\)
\(=x^4+4x^2y^2+4y^4-4x^2y^2\)
\(=\left(x^2+2y^2\right)^2-\left(2xy\right)^2\)
\(=\left(x^2+2y^2-2xy\right)\left(x^2+2y^2+2xy\right)\)
d: \(x^4+4\)
\(=x^4+4x^2+4-4x^2\)
\(=\left(x^2+2\right)^2-\left(2x\right)^2=\left(x^2+2-2x\right)\left(x^2+2+2x\right)\)
e: \(64x^4+1\)
\(=64x^4+1+16x^2-16x^2\)
\(=\left(8x^2+1\right)^2-\left(4x\right)^2=\left(8x^2+1-4x\right)\left(8x^2+1+4x\right)\)
f: \(81x^4+4\)
\(=81x^4+36x^2+4-36x^2\)
\(=\left(9x^2+2\right)^2-36x^2=\left(9x^2-6x+2\right)\left(9x^2+6x+2\right)\)
i: \(x^4-5x^2+4\)
\(=x^4-x^2-4x^2+4\)
\(=x^2\left(x^2-1\right)-4\left(x^2-1\right)=\left(x^2-1\right)\left(x^2-4\right)\)
=(x-1)(x+1)(x-2)(x+2)
