Question

find arthematic mean of (a+ b)²( a-b)²​

Answer 1

Answer:

Step-by-step explanation:

I know the answer is = 4ab, but if I could explain it…

Use the perfect square formula for each of the two expressions (a + b )² = a² + 2ab + b²

So, (a+b)² becomes a² + 2ab + b²

And, (a-b)² becomes a² - 2ab + b²

Since we are simplifying we use the distributive property method. So distribute the parentheses () in one of the expressions.

Don’t forget we are subtracting -,

thus we have the expression, a² + 2ab + b² - (a² - 2ab + b²)

Distribute the - sign in the parentheses ().

Group like terms - a² +a² + 2ab + 2ab -b²+b²

Cancel out -a²+a² and -b²+b²

Therefore∴ , 2ab + 2ab = 4ab

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Answer 2

$\huge\mathfrak\red{ANSWER}$

We know that, (a+b)² = a² + b² + 2ab

Now, we have,

(a+b)² + (a-b)²

$= (a² + b² + 2ab) + [a² + (-b)² + 2a(-b)]$

$= a² + b² + 2ab + a² + b² - 2ab$

$= 2a² + 2b²$

$= 2(a²+b²)$

Thus, we get,

$(a+b)² + (a-b)² = 2(a²+b²).$

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