Question

Разложите на множители:
(x+3y)^2-(3x-y)^2

Answer 1

(x+3y)^2-(3x-y)^2 = (x+3y-3x+y)(x+3y+3x-y)=(-2x+4y)(4x+2y)=2*(2y-x)*2*(2x+y)=4*(2y-x)(2x+y)

Answer 2

( x + 3y )² - ( 3x - y )² = ( x + 3y - ( 3x - y )) × ( x + 3y + ( 3x - y )) = ( x + 3y - 3x + y ) × ( x + 3y + 3x - y ) = ( -2x + 4y ) × ( 4x + 2y ) = ( -2 ( x - 2y )) × 2 ( 2x + y ) = - 2 × 2 ( x - 2y ) × ( 2x + y ) = - 4 ( x - 2y ) × ( 2x + y )