Question

разложите на множители
a)4x^2-(3x-2y)^2
б)x^4-2b^2x^2+b^2
в)-9c^2+12cd^2-4d^4
г)49(2m-3n)^2-9(m+n)

Answer 1

$4x^2-(3x-2y)^2=(2x+3x-2y)(2x-3x+2y)=(5x-2y)(x+2y)\\\\x^4-2b^2x+b^2=(x^2-b)^2\\\\-9c^2+12cd^2-4d^4=-(9c^2-12cd^2+4d^4)=-(3c-2d^2)^2\\\\49(2m-3n)^2-9(m+n)^2=\\=(7(2m-3n)-3(m+n))(7(2m-3n)+3(m+n))=\\=(14m-21n-3m-3n)(14m-21n+3m+3n)=\\=(11m-24n)(17m-18n)$