a.

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

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

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

b.

\(x^3+1-x^2-x\)

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

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

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

x³+2x²+x

= x ( x\(^2\) + 2x + 1 )

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

`(x+y)^3-x^3-y^3`

`=(x+y)^3-(x^3+y^3)`

`=(x+y)^3-(x+y)(x^2-xy+y^2)`

`=(x+y)[(x+y)^2-x^2+xy-y^2]`

`=(x+y)(x^2+2xy+y^2-x^2+xy-y^2)`

`=(x+y).3xy`

a) Ta có: \(\left(x+y\right)^3-x^3-y^3\)

\(=x^3-x^3+y^3-y^3+3x^2y+3xy^2\)

\(=3xy\left(x+y\right)\)

\(a,a^4+a^2+1\)

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

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

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

\(---\)

\(b,a^4+a^2-2\)

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

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

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

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

\(---\)

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

\(=x^3+2x^2-7x^2-14x\)

\(=x^2\left(x+2\right)-7x\left(x+2\right)\)

\(=\left(x+2\right)\left(x^2-7x\right)\)

\(=x\left(x+2\right)\left(x-7\right)\)

\(a.a^4+a^2+1\) 

\(=\left(a^4+2a^2+1\right)-a^2\) 

\(=\left(a^2+1\right)^2-a^2\)  

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

\(b.a^4+a^2-2\) 

\(=a^4+2a^2-a^2-2\) 

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

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

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

\(c.x^3-5x^2-14x\) 

\(=x^3+2x^2-7x^2-14\) 

\(=x^3\left(x+2\right)-7x\left(x+2\right)\) 

\(=\left(x^3-7x\right)\left(x+2\right)\) 

\(=x\left(x-7x\right)\left(x+2\right)\) 

a) 8 - 27x³

= (2 - 3x) (4 + 6x + 9x²)

b) 5x²y - 10xy - 5y²

= 5y(x² - 2x - y)

c) x³ + 8y³

= (x + 2y) (x² - 2xy + 4y²)

d) 3x² + 5y - 3xy - 5x

= (x - y) (3x - 5)

`@` `\text {Ans}`

`\downarrow`

`a,`

`3x^2 + 6xy + 3y^2 - 3z`

`= 3*x^2 + 3*2xy + 3y^2 - 3z`

`= 3(x^2 + 2xy + y^2 - z)`

`b,`

`x^3 + x^2y - x^2z - xyz`

`= x(x + y)(x-z)`