Question

Разложите на множители: 1) 81a^3- ab^2; 2) -8x^2- 16xy- 8y^2; 3) 5mn+ 15m- 10n- 30; 4) 256- b^4

Answer 1

$1)~ 81a^3-ab^2=a(81a^2-b^2)=a(9a-b)(9a+b)\\ 2)~ -8x^2-16xy-8y^2=-8(x^2+2xy+y^2)=-8(x+y)^2\\ 3)~ 5mn+15m-10n-30=5m(n+3)-10(n+3)=5(n+3)(m-2)\\ 4)~ 256-b^4=(16+b^2)(16-b^2)=(16+b^2)(4-b)(4+b)$