Question

Разложите на множители : 49с^2-14с+1-21аб+3а. ах^2+ау^2+х^4+2х^2 у^2+у^4. 27с^3-d^3+9с^2+3сd+d^2. b^3-2b^2-2b+1.

Answer 1

$49c^2-14c+1-21ac+3a=(7c-1)^2-3a(7c-1)=\\=(7c-1)(7c-1-3a)\\\\ax^2+ay^2+x^4+2x^2y^2+y^4=a(x^2+y^2)+(x^2+y^2)^2=\\=(x^2+y^2)(a+x^2+y^2)\\\\27c^3-d^3+9c^2+3cd+d^2=(3c-d)(9c^2+3cd+d)+9c^2+3cd+d=\\=(9c^2+3cd+d)(3c-d+1)\\\\(b^3-2b^2-2b+1)=(b+1)(b^2-b+1)-2(b+1)=\\=(b+1)(b^2-b+1-2)=(b+1)(b^2-b-1)$