Đáp án:

Giải thích các bước giải:

\(a,\ 125-(x+1)^3\\ =5^3-(x+1)^3\\ =(5-x-1)\left [25+5(x+1)+(x+1)^2\right ]\\ =(4-x)(25+5x+5+x^2+2x+1)\\ =(4-x)(31+7x+x^2)\\ b,\ x^3+27=x^3+3^3=(x+3)(x^2-3x+9)\\ c,\ 64-y^3=4^3-y^3=(4-y)(16+4y+y^2)\\ d,\ 8x^3-y^3=(2x)^3-y^3=(2x-y)(4x^2+2xy+y^2)\\ e,\ 125x^3-64y^3=(5x)^3-(4y)^3=(5x-4y)(25x^2+20xy+16y^2)\\ f,\ -x^2+2x-1=-(x^2-2x+1)=-(x-1)^2\\ g,\ x^3-6x^2+9x=x(x^2-6x+9)=x(x-3)^2\\ h,\ x^3-49x=x(x^2-49)=x(x-7)(x+7)\)

chúc em học tốt!

Đáp án:

$\begin{array}{l}
a)125 - {\left( {x + 1} \right)^3}\\
 = {5^3} - {\left( {x + 1} \right)^3}\\
 = \left( {5 - x - 1} \right)\left( {{5^2} + 5\left( {x + 1} \right) + {{\left( {x + 1} \right)}^2}} \right)\\
 = \left( {4 - x} \right)\left( {31 + 5x + {x^2} + 2x} \right)\\
 = \left( {4 - x} \right)\left( {{x^2} + 7x + 31} \right)\\
b){x^3} + 27\\
 = {x^3} + {3^3}\\
 = \left( {x + 3} \right)\left( {{x^2} - 3x + 9} \right)\\
c)64 - {y^3}\\
 = \left( {4 - y} \right)\left( {16 + 4y + {y^2}} \right)\\
d)8{x^3} - {y^3}\\
 = \left( {2x - y} \right)\left( {4{x^2} + 2xy + {y^2}} \right)\\
e)125{x^3} - 64{y^3}\\
 = \left( {5x - 4y} \right)\left( {25{x^2} + 20xy + 16{y^2}} \right)\\
f) - {x^2} + 2x - 1\\
 =  - \left( {{x^2} - 2x + 1} \right)\\
 =  - {\left( {x - 1} \right)^2}\\
g){x^3} - 6{x^2} + 9x\\
 = x\left( {{x^2} - 6x + 9} \right)\\
 = x{\left( {x - 3} \right)^2}\\
h){x^3} - 49x\\
 = x\left( {{x^2} - 49} \right)\\
 = x\left( {x - 7} \right)\left( {x + 7} \right)
\end{array}$