Question

prove (a^2+b^2)=(a+b)^2-2ab=(a-b)^2+2ab​

Answer 1

Step-by-step explanation:

To prove:-

(a^2+b^2)=(a+b)^2-2ab=(a-b)^2+2ab

Let us split it

i)Lets prove (a^2+b^2)=(a+b)^2-2ab

We know that,

${(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab$

So, (a+b)^2 - 2ab = a^2 + b^2 + 2ab - 2ab

2ab gets cancelled

= a^2 + b^2

Hence , proved

ii) Let's prove a^2 + b^2 = (a-b)^2 + 2ab

We know that,

${(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab$

So, (a-b)^2+2ab = a^2 + b^2 -2ab + 2ab

2ab gets cancelled

= a^2 + b^2

Hence, proved

Hence proved that, (a^2+b^2)=(a+b)^2-2ab=(a-b)^2+2ab

Hope this answer is helpful

Sathvik✍️