Question

Упростите выражение:

а) (n+1)(2n-3)+(n-1)(3n+1)

б) (x-y)(2x-3y)-(3x-y)(2x+y)

в) (2a+3)(2a+3)-(2a+1)(2a-1)

г) (3c-d)(d+3c)+(4c-d)(c-4d)

Answer 1

$a) (n+1)(2n-3)+(n-1)(3n+1)=\ =2n^2-n-3+3n^2-2n-1=\ =5n^2-3n-4\ b) (x-y)(2x-3y)-(3x-y)(2x+y)=\ =2x^2-5xy+3y^2-(6x^2+xy-y^2)=\ =2x^2-5xy+3y^2-6x^2-xy+y^2=\ =-4x^2-6xy+4y^2\ c) (2a+3)(2a+3)-(2a+1)(2a-1)=\ =(2a+3)^2-(2a)^2+1=4a^2+12a+9-4a^2+1=\ =12a+10\ d) (3c-d)(d+3c)+(4c-d)(c-4d)=\ =(3c)^2-d^2+4c^2-17cd+4d^2=\ =9c^2-d^2+4c^2-17cd+4d^2=\ =13c^2-17cd+3d^2$