Question

25 баллов (1/8x^3-7/8)^2

Answer 1

Ответ:

$( \frac{1}{8} x {}^{3} - \frac{7}{8} ) {}^{2} = ( \frac{1}{8} x {}^{3}) {}^{2} - 2 \times \frac{1}{8} x {}^{3} \times \frac{7}{8} +( \frac{7}{8} ) {}^{2} = \frac{1}{64}x {}^{6} - \frac{7}{32} x {}^{3} + \frac{49}{64}$

Answer 2

To calculate the expression, let's first simplify it step by step:

1. Start with the given expression: 25(1/8x^3 - 7/8)^2

2. Square the expression inside the parentheses: (1/8x^3 - 7/8)^2 = (1/8x^3 - 7/8)(1/8x^3 - 7/8)

3. Apply the formula for squaring a binomial (a - b)^2 = a^2 - 2ab + b^2: (1/8x^3 - 7/8)(1/8x^3 - 7/8) = (1/8x^3)^2 - 2 * (1/8x^3) * (7/8) + (-7/8)^2

4. Simplify the expression: (1/8x^3)^2 = (1/8)^2 * x^6 = 1/64 * x^6 (-7/8)^2 = (-7/8) * (-7/8) = 49/64

5. Put it all together: (1/8x^3 - 7/8)^2 = 1/64 * x^6 - 2 * (1/8x^3) * (7/8) + 49/64

6. Simplify further, keeping the common denominator: (1/8x^3 - 7/8)^2 = (1/64) * x^6 - (14/64) * x^3 + 49/64

Now, multiply this simplified expression by 25:

25 * [(1/64) * x^6 - (14/64) * x^3 + 49/64]

Finally, distribute the 25 into each term:

(25/64) * x^6 - (350/64) * x^3 + (1225/64)

So, the simplified expression for 25(1/8x^3 - 7/8)^2 is (25/64) * x^6 - (350/64) * x^3 + (1225/64).