Question

Сократите дробь:
2а⁴в³+8а³в⁴+8а²в^5:5а²в²+10ав³

Answer 1

$\frac{2a^4b^3+8a^3b^4+8a^2b^5}{5a^2b^2+10ab^3} = \frac{2a^2b^3(a^2+4ab+4b^2)}{5ab^2(a+2b)} = \frac{2a^2b^3(a^2+2*a*2b+(2b)^2)}{5ab^2(a+2b)}= \\ \\ = \frac{2a^2b^3(a+2b)^2}{5ab^2(a+2b)} = \frac{2ab(a+2b)}{5} = \frac{2}{5} *ab(a+2b)= \\ \\ = 0.4ab(a+2b) = 0.4a^2b + 0.8ab^2$