What should be added to a² + 2ab + b² to get 4ab + b² ? (write the ans with steps)

Hi

Let p be the required term

a² + 2ab + b² + p = 4ab + b²

p = 4ab + b² - (a² + 2ab +b²)

Open the brackets

4ab + b² - a² - 2ab - b²

Now combine like terms

4ab -2ab + b² - b² - a²

= 2ab -a²

Lets check

a² + 2ab + b² + 2ab - a²

Now combine like terms

2ab+ 2ab  + 1a² - 1a² + b²

= 4ab + 0 + b²

So the answer is 2ab - a²

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