Bài 10:

a: \(\left(x^2+4x+8\right)^2+3x^{}\left(x^2+4x+8\right)+2x^2\)

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

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

\(=\left(x+4\right)\left(x+2\right)\left(x^2+5x+8\right)\)

b: abc-(ab+ac+bc)+(a+b+c)-1

=abc-ab-ac-bc+a+b+c-1

=ab(c-1)-a(c-1)-b(c-1)+(c-1)

=(c-1)(ab-a-b+1)

=(c-1)(b-1)(a-1)

Bài 8:

a: \(x^4+4\)

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

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

b: \(4x^8+1=4x^8+4x^4+1-4x^4\)

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

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

c: \(81x^4+4\)

\(=81x^4+36x^2+4-36x^2\)

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

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

d: \(64x^4+y^4\)

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

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

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

e: \(\left(x^2-8\right)^2+36\)

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

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

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

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

f: \(\left(2x^2-4\right)_{}^2+9\)

\(=4x^4-16x^2+16+9\)

\(=4x^4-16x^2+25\)

\(=4x^4+20x^2+25-36x^2\)

\(=\left(2x^2+5\right)^2-\left(6x\right)^2=\left(2x^2+5-6x\right)\left(2x^2+5+6x\right)\)