Question

Разложите на множители: 1)1000m³-n³ 2)81a³-ab² 3)-8x²-16xy-8y² 4)5mn+15m-10n-30 5)256-b⁴

Answer 1

$1000m^3-n^3=(10m-n)(100m^2+10mn+n^2)\\\\81a^3-ab^2=a(81a^2-b^2)=a(9a-b)(9a+b)\\\\5mn+15m-10n-30=5(mn+3m-2n-6)=\\=5(m(n+3)-2(n+3)+n(m-2)+3(m-2))=5(m-2)(n+3)\\\\-8x^2-16xy-8y^2=-2(4x^2+8xy+4y^2)=-2(2x+2y)^2\\\\256-b^4=4^4-b^4=(16+b^2)(16-b^2)$