Question

Розкладіть на множники будь-ласка

Answer 1

$\displaystyle\bf\\1)\\\\\frac{16}{49} a^{2} -(a-5b)^{2} =\Big(\frac{4}{7} a\Big)^{2} -(a-5b)^{2} =\\\\\\=\Big(\frac{4}{7} a-a+5b\Big)\cdot\Big(\frac{4}{7} a+a-5b\Big)=\\\\\\=\Big(5b-\frac{3}{7} a\Big)\cdot\Big(1\frac{4}{7} a-5b\Big)\\\\2)\\\\9x^{4} +x^{2} y+\frac{1}{36} y^{2} =\Big(3x^{2} \Big)^{2} +2\cdot 3x^{2} \cdot\frac{1}{6} y+\Big(\frac{1}{6} y\Big)^{2} =\\\\\\=\Big(3x^{2} +\frac{1}{6} y\Big)^{2} =\Big(3x^{2} +\frac{1}{6} y\Big)\cdot\Big(3x^{2} +\frac{1}{6} y\Big)$

$\displaystyle\bf\\3)\\\\(3a+4)^{3} -125=(3a+4)^{3} -5^{3} =\\\\\\=(3a+4-5)\cdot\Big[(3a+4)^{2} +5\cdot(3a+4)+5^{2} \Big]=\\\\\\=(3a-1)\cdot(9a^{2} +24a+16+15a+20+25)=\\\\\\=(3a-1)\cdot(9a^{2} +39a+61)$