Question

(√10 + 3√2)² (3√8-2³√2)(3√8+2³√2)

Answer 1

(√10 + 3√2)² - возводим в квадрат = 10+18=28.

(3√8-2³√2)(3√8+2³√2)= (6√2-8√2)*(6√2+8√2)= -56

Answer 2

раскроем как квадрат суммы по формуле ускоренного умножения (√10+3√2)^2=10+2*3*√10*√2+18=28+6√20=28+12√5

Произведение суммы двух чисел на их разность равен разности квадратов этих чисел:

(3√8-2^3*√2)(3√8-2^3*√2)=(3√8)^2-(2^3*√2)^2=72-128=-56

Answer 3

Let's simplify the given expression step by step.

Step 1: Simplify the first part - (√10 + 3√2)² To square a binomial (a + b)², we use the formula: (a + b)² = a² + 2ab + b²

Let a = √10 and b = 3√2: (√10 + 3√2)² = (√10)² + 2(√10)(3√2) + (3√2)² = 10 + 2√20 + 18 = 28 + 2√20

Step 2: Simplify the second part - (3√8 - 2³√2) Here, we can't simplify it further, as the terms are not like terms.

Step 3: Simplify the third part - (3√8 + 2³√2) Again, we can't simplify it further, as the terms are not like terms.

Step 4: Combine the three parts together The given expression becomes:

(√10 + 3√2)² (3√8 - 2³√2)(3√8 + 2³√2) = (28 + 2√20)(3√8 - 2³√2)(3√8 + 2³√2)

We can't simplify it further unless we know the values of √20, √8, and √2. If you have specific values for these square roots, please provide them, and I can help you simplify the expression further.