Question

Помогите пожалуйста, разложить на множители

Answer 1

$a^3+27=a^3+3^3=(a+3)(a^2-3a+9)\\\\8x^3-216=8*(x^3-27)=8*(x^3-3^3)=8*(x-3)(x^2+3a+9)\\\\1-p^6=1^3-(p^2)^3=(1-p^2)(1+p^2+p^4)\\\\2\frac{10}{27}p^3+q^3=\frac{64}{27}p^3+q^3=(\frac{4}{3}p)^3+q^3=\\\\=(\frac{4}{3}p+q)(\frac{16}{9}p^2-\frac{4}{3}pq+q^2);$

$a^3+b^6=a^3+(b^2)^3=(a+b^2)(a^2-ab^2+b^4)\\\\125x^6-y^3=(5x^2)^3-y^3=(5x^2-y)(25y^2+5x^2y+y^2)\\\\\\\frac{1}{125}x^6-\frac{1}{8}y^9=(\frac{1}{5}x^2)^3-(\frac{1}{2}y^3)^3=\\\\=(\frac{1}{5}x^2-\frac{1}{2}y^3)(\frac{1}{25}x^4+\frac{1*1}{5*2}x^2y^3+\frac{1}{4}y^6)=\\\\=(\frac{1}{5}x^2-\frac{1}{2}y^3)(\frac{1}{25}x^4+\frac{1}{10}x^2y^3+\frac{1}{4}y^6)$