Question

Докажите тождество:

( а + b)^2 - (a - b)^2 = 4ab

Answer 1

$(a+b)^2-(a-b)^2=(a^2+2ab+b^2)-(a^2-2ab+b^2)=\\=a^2+2ab+b^2-a^2+2ab-b^2=4ab\\4ab=4ab$

Answer 2

$( a+b)^2 - (a - b)^2 = 4ab \ (a+b-(a-b))(a+b+a-b) = 4ab \ (a+b-a+b)*2a = 4ab \ 2b*2a = 4ab$