Question

а²(а² +5а -1)- 3а(а³ + 5а² - а) +2+ 20а³ - 2а² , якщо а = ⅓

Answer 1

$\displaystyle\bf\\a^{2} (a^{2} +5a-1)-3a(a^{3} +5a^{2} -a)+2+20a^{3} -2a^{2}=\\\\\\=a^{4}+5a^{3} -a^{2} -3a^{4} -15a^{3}+3a^{2} +2+20a^{3} -2a^{2} =\\\\\\=\underbrace{(a^{4} -3a^{4} )}_{-2a^{4} }+\underbrace{(5a^{3} -15a^{3} +20a^{3})}_{10a^{3}} -\underbrace{(a^{2} -3a^{2} +2a^{2} )}_{0}+2=\\\\\\=-2a^{4} +10a^{3} +2\\\\\\a=\frac{1}{3} \\\\\\-2a^{4} +10a^{3} +2=-2\cdot\Big(\frac{1}{3} \Big)^{4} +10\cdot\Big(\frac{1}{3} \Big)^{3} +2=$

$\displaystyle\bf\\=-2\cdot\frac{1}{81} +10\cdot\frac{1}{27}+2=-\frac{2}{81} +\frac{10}{27} +2= \\\\\\=\frac{-2+10\cdot3}{81} +2=\frac{28}{81} +2=2\frac{28}{81}$