a: Ta có: \(a^5-ax^4+a^4x-x^5\)

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

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

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

\(4\left(x^2y^2+z^2t^2+2xyzt\right)-\left(x^2+y^2-z^2-t^2\right)^2\)

\(=\left(2xy-2tz\right)^2-\left(x^2+y^2-z^2-t^2\right)\)

\(=\left(2xy-2tz-x^2-y^2+z^2+t^2\right)\left(2xy-2tz+x^2+y^2-z^2-t^2\right)\)

\(=\left[-\left(x-y\right)^2+\left(z-t\right)^2\right]\left[\left(x+y\right)^2-\left(t+z\right)^2\right]\)

\(=-\left(x-y-z+t\right)\left(x-y+z-t\right)\left(x+y-t-z\right)\left(x+y+t+z\right)\)

x²-2xy+y²+3x-3y-10

= (x-y)²+3(x-y)-10

= [(x-y)²+5(x-y)]-[2(x-y)+10]

= (x-y)(x-y+5)-2(x-y+5)

= (x-y+5)(x-y-2)

Ta có: \(x^2-2xy+y^2+3x-3y-10\)

\(=\left(x-y\right)^2+3\left(x-y\right)-10\)

\(=\left(x-y+5\right)\left(x-y-2\right)\)

=3x(x+2y)

=3x(x+2y)

3x² + 6xy

= 3x(x+2y)

\(2x^2+x-6\)

\(=2x^2-3x+4x-6\)

\(=x\left(2x-3\right)+2\left(2x-3\right)\)

\(=\left(2x-3\right)\left(x+2\right)\)

Tham Khảo

2x² + x - 6

= 2x² + 4x - 3x - 6

= 2x(x + 2) - 3(x - 2)

= (2x - 3)(x + 2)

\(6x^2-13x+6\)

\(=6x^2-9x-4x+6\)

\(=\left(2x-3\right)\left(3x-2\right)\)

x²-2x-15=(x²-5x)+(3x-15)=x(x-5)+3(x-5)=(x-5)(x+3)

\(x^2-3x-15=\left(x^2-2.\dfrac{3}{2}x+\dfrac{9}{4}\right)-\dfrac{69}{4}=\left(x-\dfrac{3}{2}\right)^2-\left(\dfrac{\sqrt{69}}{2}\right)^2\)

\(=\left(x-\dfrac{3}{2}-\dfrac{\sqrt{69}}{2}\right)\left(x-\dfrac{3}{2}+\dfrac{\sqrt{69}}{2}\right)\)

\(x^2-2x-15=\left(x-5\right)\left(x+3\right)\)

\(3x^2-14x-5=3x\left(x-5\right)+\left(x-5\right)=\left(x-5\right)\left(3x+1\right)\)

\(3x^2-14x-5\)

\(=3x^2-15x+x-5\)

\(=3x\left(x-5\right)+x-5\)

\(=\left(x-5\right)\left(3x+1\right)\)

A= 3x^2 + 14x - 15
3A= (3x)^2 + 2.7.(3x) - 15.3
3A= (3x+7)^2 +(15.3-7.7)
3A= (3x+7 )^2 -2^2
3A= (3x+7-2 )((3x+7+2 )
A= ( 3x-5)( x+ 3)

x⁵-x⁴-30x³=x³(x²-x-30) = x³(x-6)(x+5) 

\(x^5-x^4-30x^3=x^3\left(x^2-x-30\right)=x^3\left(x-6\right)\left(x+5\right)\)

\(x^5-x^4-30x^2=x^2\left(x^2-x-30\right)=x^2\left(x+5\right)\left(x-6\right)\)