Question

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

Answer 1

Ответ:

1

Объяснение:

Раскрываешь скобки в числителе по формулам сокращенного умножения и сокращаешь одинаковые значения, получаешь 1

Answer 2

Let's simplify the expression step by step:

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

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

Now, let's substitute these values back into the original expression:

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

Next, let's simplify the expression by combining like terms:

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

Now, let's simplify further:

= 2a^2 + 2b^2

Finally, let's simplify the denominator of the fraction:

a^2 + b^2 + a^2 + b^2 = 2a^2 + 2b^2

Now, we can rewrite the expression:

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

Notice that the numerator and denominator have the same terms, so they cancel out:

= 1

Therefore, the expression simplifies to 1.