32. Khai triển các biểu thức sau:
a) $(4x + 1)^{4}$;
b) $(5x – 3)^{4}$;
c) $(\frac{1}{3}x+5)^{5}$
d) $(3x-\frac{1}{3})^{5}$
Bài Làm:
a) $(4x + 1)^{4} = (4x)^{4} + 4\times (4x)^{3}\times 1 + 6\times (4x)^{2}\times 1^{2} + 4\times 4x\times 1^{3} + 1^{4}$
= $256x^{4} + 256x^{3} + 96x^{2} + 16x + 1.$
b) $(5x – 3)^{4} = (5x)^{4} + 4\times (5x)^{3}\times (–3) + 6\times (5x)^{2}\times (–3)^{2}+ 4\times 5x\times (–3)^{3} + (–3)^{4}$
= $625x^{4} – 1500x^{3} + 1350x^{2} – 540x + 81.$
c) $(\frac{1}{3}+5)^{5}=(\frac{1}{3}x)^{5}+5\times (\frac{1}{3}x)^{4}\times 5+10\times (\frac{1}{3}x)^{3}\times 5^{2}+10\times (\frac{1}{3}x)^{2}\times 5^{3}+5\times (\frac{1}{3}x)\times 5^{4}+5^{5}$
$= \frac{1}{243}x^{5}+\frac{25}{81}x^{4}+\frac{250}{27}x^{3}+\frac{1250}{9}x^{2}+\frac{3125}{3}x+3125$
d) $(3x-\frac{1}{3})^{5}=(3x)^{5}+5\times (3x)^{4}\times (-\frac{1}{3})+10\times (3x)^{3}\times (-\frac{1}{3})^{2}+10\times (3x)^{2}\times (-\frac{1}{3})^{3}+5\times (3x)\times (-\frac{1}{3})^{4}+5\times (-\frac{1}{3})^{5}$
$=243x^{5}-135x^{4}+30x^{3}-\frac{10}{3}x^{2}+\frac{5}{27}x-\frac{1}{243}$