Question

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

Answer 1

1)$1000m^3-n^3=(10m-n)(100m^2+10mn+n^2)$

2)$81a^3-ab^2=a(81a^2-b^2)=a(9a-b)(9a+b)$

3)$-8x^2-16xy-8y^2=-8(x^2+2xy+y^2)=-8(x+y)^2$

4)$5mn+15m-10n-30=5n(m-2)+15(m-2)=(5n+15)(m-2)=\5(n+3)(m-2)$

5)$256-b^4=4^4-b^4=(4^2-b^2)(4^2+b^2)=(4+b)(4-b)(16+b^2)$