Question

Разложить на множетели

Answer 1

$1 \frac{24}{25} m ^{6} n ^{4} - 1 \frac{9}{16} {a}^{2} {b}^{8} = \\ = \frac{49}{25} m ^{6} n ^{4} - \frac{25}{16} {a}^{2} {b}^{8} = \\ = (\frac{7}{5} m ^{3} n ^{2} )^{2} - (\frac{5}{4} {a} {b}^{4} ) ^{2} = \\ = (\frac{7}{5} m ^{3} n ^{2} - \frac{5}{4} {a} {b}^{4} ) (\frac{7}{5} m ^{3} n ^{2} + \frac{5}{4} {a} {b}^{4} )$

Answer 2

$1\frac{24}{25}m^6n^4-1\frac{9}{16}a^2b^8=\frac{49}{25}m^6n^4-\frac{25}{16}a^2b^8=(\frac{7}{5}m^3n^2)^2-(\frac{5}{4}ab^4)^2=\\\\=(\frac{7}{5}m^3n^2-\frac{5}{4}ab^4)\cdot (\frac{7}{5}m^3n^2+\frac{5}{4}ab^4)$