Question

simplify (a+b+c)²-(a-b-c)²​

Answer 1

Answer:

(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca

Consider, (a+b+c)2 – (a – b – c)2+ 4b2– 4c2

= a2 + b2 + c2 + 2ab + 2bc + 2ca – (a2 + b2 + c2 – 2ab + 2bc – 2ca)+ 4b2– 4c2

= a2 + b2 + c2 + 2ab + 2bc + 2ca – a2 – b2 – c2 + 2ab – 2bc +2ca + 4b2– 4c2

= 4ab + 4ca + 4b2– 4c2

= 4(ab + ca + b2– c2)

= 4[a(b + c) +(b2– c2)]

= 4[a(b + c) + (b + c)(b – c)]

= 4(b + c)(a + b – c)

Answer 2

Answer:0

Step-by-step explanation:

(a+b+c)^2-(a-b-c)^2

=a^2+b^2+c^2 - a^2-b^2-c^2

= a^2-a^2 + b^2-b^2 + c^2-c^2

=0+0+0(because all cut each other

=0