Đáp án:
$\displaystyle \begin{array}{{>{\displaystyle}l}} a.a^{3} +9a^{2} +27a+27\\ b.27x^{3} +27x^{2} +9x+1\\ c.125x^{3} +150x^{2} y+60xy^{2} +8y^{3}\\ d.x^{3} -3x^{2} +3x-1\\ e.27x^{3} -54x^{2} y+36xy^{2} -8y^{3}\\ f.27-108y^{2} +144y^{4} -64y^{6}\\ g.9x^{2} -1\\ h.4a^{2} -\frac{1}{4}\\ i.4a^{4} -9b^{2} \end{array}$
Giải thích các bước giải:
$\displaystyle \begin{array}{{>{\displaystyle}l}} a.( a+3)^{3} =a^{3} +3a^{2} .3+3.3^{2} .a+3^{3} =a^{3} +9a^{2} +27a+27\\ b.\ ( 3x+1)^{3} =( 3x)^{3} +3.( 3x)^{2} .1+3.3x.1^{2} +1^{3} =27x^{3} +27x^{2} +9x+1\\ c.\ ( 5x+2y)^{3} =( 5x)^{3} +3.( 5x)^{2} .2y+3.( 2y)^{2} .5x+( 2y)^{3}\\ =125x^{3} +150x^{2} y+60xy^{2} +8y^{3}\\ d.\ ( x-1)^{3} =x^{3} -3x^{2} .1+3.1^{2} .x-1^{3} =x^{3} -3x^{2} +3x-1\\ e.\ ( 3x-2y)^{3} =( 3x)^{3} -3.( 3x)^{2} .2y+3.( 2y)^{2} .3x-( 2y)^{3}\\ =27x^{3} -54x^{2} y+36xy^{2} -8y^{3}\\ f.\ \left( 3-4y^{2}\right)^{3} =3^{3} -3.3^{2} .\left( 4y^{2}\right) +3.\left( 4y^{2}\right)^{2} .3-\left( 4y^{2}\right)^{3}\\ =27-108y^{2} +144y^{4} -64y^{6}\\ g.\ ( 3x+1)( 3x-1) =( 3x)^{2} -1^{2} =9x^{2} -1\\ h.\ \left( 2a+\frac{1}{2}\right)\left( 2a-\frac{1}{2}\right) =( 2a)^{2} -\left(\frac{1}{2}\right)^{2} =4a^{2} -\frac{1}{4}\\ i.\ \left( 2a^{2} -3b\right)\left( 2a^{2} +3b\right) =\left( 2a^{2}\right)^{2} -( 3b)^{2} =4a^{4} -9b^{2} \end{array}$
