a) \(a^5+a^3-a^2-1\)

\(=a^5+a^4+a^3+a^3+a^2+a-a^4-a^3-a^2-a^2-a-1\) 

\(=a^3\left(a^2+a+1\right)+a\left(a^2+a+1\right)-a^2\left(a^2+a+1\right)-\left(a^2+a+1\right)\)

\(=\left(a^3+a-a^2-1\right)\left(a^2+a+1\right)\)

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

\(=\left[\left(a-1\right)\left(a^2+a+1\right)-a\left(a-1\right)\right]\left(a^2+a+1\right)\)

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

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

b) \(27a^2b^2-18ab+3\)

\(=3\left(9a^2b^2-6ab+1\right)\)

\(=3\left(3ab-1\right)^2\)

c) \(4-x^2-2xy-y^2\)

 \(=4-\left(x+y\right)^2\)

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

Cam on nhe

\(ab\left(x^2+y^2\right)-xy\left(a^2+b^2\right)\)

\(=abx^2+aby^2-a^2xy-b^2xy\)

\(=ax\left(bx-ay\right)+by\left(ay-bx\right)\)

\(=ax\left(bx-ay\right)-by\left(bx-ay\right)\)

\(\left(bx-ay\right)\left(ax-by\right)\)

hãy k nếu bạn thấy đây là câu tl đúng :)

Thanks 

Ta có:

\(x^3+2x^2+x+2\)

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

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

x³+2x²+x+2=x²(x+2)+(x+2)

                  =(x²+1)(x+2)

cam on ban nhieu lam

x ² - 2007x - 2008

= x ² + x - 2008x - 2008

= ( x ² + x ) - ( 2008x + 2008 )

= x ( x + 1 ) - 2008 . ( x + 1 )

= ( x + 1 ) . ( x - 2008 )

x²-xy-2y²

= x²-2xy+xy-2y²

=x(x-2y)+y(x-2y)

=(x-2y)(x+y)

ab(a+b)+bc(b+c)+ca(c+a)+3abc

=(ab(a+b)+abc)+(bc(b+c)+abc)+(ca(c+a)+abc)

=ab(a+b+c)+bc(b+c+a)+ca(c+a+b)

=(a+b+c)(ab+bc+ca)