Đáp án `+` Giải thích các bước giải `!`

`e)`

`E= ax-bx+ab-x^2`

`= (ax+ab)-(bx+x^2)`

`= a(x+b)-x(b+x)`

`= (a-x)(x+b)`

`f)`

`F= xy-8x-8y+y^2`

`= (xy+y^2)-(8x+8y)`

`= y(x+y)-8(x+y)`

`= (y-8)(x+y)`

`g)`

`G= 8x^3-(1)/(125)y^3`

`= (2x)^3-((1)/(5)y)^3`

`= (2x-(1)/(5)y)(4x^2+(2)/(5)xy+(1)/(25)y^2)`

Áp dụng: `a^3-b^3 = (a-b)(a^2+ab+b^2)`

`h)`

`H= 2-25x^4`

`= \sqrt{2^2}-(5x^2)^2`

`= (\sqrt{2}-5x^2)(\sqrt{2}+5x^2)`

Áp dụng: `a^2-b^2 = (a-b)(a+b)`

Đáp án:

$\begin{array}{l}
a)A = 24x - 18y + 30\\
 = 6.\left( {4x - 3y + 5} \right)\\
b)B = 4{x^2}{y^2} + 36{x^2}{y^3} + 6x{y^4}\\
 = 2x{y^2}\left( {2x + 18xy + 3{y^2}} \right)\\
c)C = 2{a^2}{y^4} + 12{a^4}y + 6{a^3}{y^3}\\
 = 2{a^2}y\left( {{y^3} + 4{a^2} + 3a{y^2}} \right)\\
d)D = 2xy - 4x + 5{y^2} - 10y\\
 = 2xy + 5{y^2} - 4x - 10y\\
 = y\left( {2x + 5y} \right) - 2\left( {2x + 5y} \right)\\
 = \left( {2x + 5y} \right)\left( {y - 2} \right)\\
e)E = a.x - bx + ab - {x^2}\\
 = a.x - {x^2} + ab - bx\\
 = x.\left( {a - x} \right) + b\left( {a - x} \right)\\
 = \left( {a - x} \right)\left( {x + b} \right)\\
f)F = xy - 8x - 8y + {y^2}\\
 = x\left( {y - 8} \right) + y\left( {y - 8} \right)\\
 = \left( {y - 8} \right)\left( {x + y} \right)\\
g)G = 8{x^3} - \dfrac{1}{{125}}{y^3}\\
 = \left( {2x - \dfrac{1}{5}y} \right)\left( {4{x^2} + \dfrac{2}{5}xy + \dfrac{1}{{25}}{y^2}} \right)\\
h)H = 2 - 25{x^4}\\
 = \left( {\sqrt 2  - 5{x^2}} \right)\left( {\sqrt 2  + 5{x^2}} \right)
\end{array}$