thực hiện các phép tính sau: a, (x+5)(x^2-5x+25) b, (y+3x)(9x^2-3xy+y^2) c, (x+1/3)(x² -1/3.x+1/9) d, (3/4.x+y³)(-9/16.x²+3/4.xy ³-y^6)

Đáp án:

$\begin{array}{l}
a)\left( {x + 5} \right)\left( {{x^2} – 5x + 25} \right)\\
 = {x^3} + {5^3}\\
 = {x^3} + 125\\
b)\left( {y + 3x} \right)\left( {9{x^2} – 3xy + {y^2}} \right)\\
 = {\left( {3x} \right)^3} + {y^3}\\
 = 27{x^3} + {y^3}\\
c)\left( {x + \dfrac{1}{3}} \right)\left( {{x^2} – \dfrac{1}{3}x + \dfrac{1}{9}} \right)\\
 = {x^3} + {\left( {\dfrac{1}{3}} \right)^3}\\
 = {x^3} + \dfrac{1}{{27}}\\
d)\left( {\dfrac{3}{4}x + {y^3}} \right)\left( {\dfrac{{ – 9}}{{16}}{x^2} + \dfrac{3}{4}x{y^3} – {y^6}} \right)\\
 =  – \left( {\dfrac{3}{4}x + {y^3}} \right)\left( {\dfrac{9}{{16}}{x^2} – \dfrac{3}{4}x{y^3} + {y^6}} \right)\\
 =  – {\left( {\dfrac{3}{4}x} \right)^3} – {\left( {{y^3}} \right)^3}\\
 =  – \dfrac{{27}}{{64}}{x^3} – {y^9}
\end{array}$