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\(x^4-x+2008x^2+2008x+2008\)
\(=x\left(x^3-1\right)+2008\left(x^2+x+1\right)\)
\(=x\left(x-1\right)\left(x^2+x+1\right)+2008\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left(x^2-x+2008\right)\)
\(B=x^4+3x^3-x^2+3x^3+9x^2-3x-x^2-3x+1\)
\(=\left(x^2+3x-1\right)^2\)
\(a^6+a^4+a^2b^2+b^4-b^6\)
\(=(a^2)^3-(b^2)^3+(a^4+a^2b^2+b^4)\)
\(=(a^2-b^2)(a^4+a^2b^2+b^4)+(a^4+a^2b^2+b^4)\)
\(=(a^2-b^2+1)(a^4+a^2b^2+b^4)\)
\(=(a^4+2a^2b^2+b^4-a^2b^2)(a^2-b^2+1)\)
\(=(a^2+ab+b^2)(a^2-ab+b^2)(a^2-b^2+1)\)
\(a^6+a^2b^2+a^4+b^2-b^6\)
\(=a^4\left(a^2+b^2\right)+a^2\left(a^2+b^2\right)-b^6\)
\(=\left(a^2+b^2\right)+\left(a^4+a^2\right)-b^6\)
Sửa đề: \(x^4+x^2+1\)
\(=x^4+2x^2+1-x^2\)
\(=\left(x^2+1\right)^2-x^2\)
\(=\left(x^2+x+1\right)\left(x^2-x+1\right)\)
x\(^2\)-(a+b)x+ab
= x\(^2\)-ax-bx+ab
= x(x-a) - b(x-a)
= ( x-a).( x-b)
ax-2x-a\(^2\)+2a
= x(a-2) - a(a-2)
= (a-2).( x-a)
a, x^2 + 7x + 6
= x^2 + x + 6x + 6
= x(x + 1) + 6(x + 1)
= (x + 6)(x + 1)
\(x^2+7x+6\)
\(=x^2+x+6x+6\)
\(=x\left(x+1\right)+6\left(x+1\right)\)
\(=\left(x+6\right)\left(x+1\right)\)