Question

разложите на множители a^2-36b^2+72cb-36c^2

Answer 1

$a^2-36b^2+72cb-36c^2=a^2+(-36)*b^2-(-36)*2cb+(-36)*c^2=$

$=a^2-36(b^2-2bc+c^2)=a^2-6^2(b-c)^2=a^2-[6(b-c)]^2=$

$=a^2-[6(b-c)]^2=[a-6(b-c)]*[a+6(b-c)]=$

$=(a-6b+6c)(a+6b-6c)$