Question

Find the middle term of the expansion of (√x+√y)^8. a. 40x2y2 c. 40x4y4 b. 70x2y2 d. 70x4y4

Answer 1

The middle term of the expansion of (√x + √y)⁸ is; B: 70 * x² * y²

How to solve binomial theorems?

We want to expand the expression;

(√x + √y)⁸

Now, according to binomial expansion, we know that;

(x + y)ⁿ = ⁿC₀ xⁿ y⁰ + ⁿC₁ xⁿ ⁻ ¹ y¹ + ⁿC₂ xⁿ ⁻ ² y² + ..... + ⁿCₙ x⁰ yⁿ.

Now, for an 8 power binomial, the coefficient of each term from formula are respectively;

1      8      28      56      70     56     28    8      1

The mid term is the fifth term and so, we have;

(⁸C₄ * (√x)⁽⁸ ⁻ ⁴⁾ * (√y)⁴)

⇒ 70 * x² * y²

Read more about Binomial theorems at; brainly.com/question/13602562

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