Question

(10 - 3r)³ преобразовать в многочлен

Answer 1

Ответ: вот ответ

Объяснение:

Answer 2

Converting the Expression (10 - 3r)³ into a Polynomial

To convert the expression (10 - 3r)³ into a polynomial, we need to expand it using the binomial theorem. The binomial theorem states that for any real numbers a and b, and any positive integer n, the expansion of (a + b)ⁿ can be written as the sum of terms of the form C(n, k) * a^(n-k) * b^k, where C(n, k) represents the binomial coefficient.

In this case, we have (10 - 3r)³. Let's expand it step by step:

Step 1: Apply the binomial theorem to the first term (10)³: (10)³ = 1 * 10³ = 1000

Step 2: Apply the binomial theorem to the second term (-3r)³: (-3r)³ = (-3)³ * r³ = -27r³

Step 3: Apply the binomial theorem to the cross terms: -3 * (10)² * (3r) = -3 * 100 * 3r = -900r

Step 4: Apply the binomial theorem to the cross terms: -3 * 10 * (3r)² = -3 * 10 * 9r² = -270r²

Step 5: Apply the binomial theorem to the cross terms: (10) * (-3r)² * (-3) = 10 * 9r² * (-3) = -270r²

Step 6: Apply the binomial theorem to the cross terms: (10) * (3r) * (-3r) = 10 * 3r * (-3r) = -90r²

Step 7: Apply the binomial theorem to the cross terms: (10)² * (-3r) * (-3) = 100 * (-3r) * (-3) = 900r

Step 8: Apply the binomial theorem to the cross terms: (10)² * (3r)² = 100 * 9r² = 900r²

Step 9: Apply the binomial theorem to the cross terms: (10) * (3r) * (-3) = 10 * 3r * (-3) = -90r

Step 10: Apply the binomial theorem to the cross terms: (10) * (-3r) * (-3) = 10 * (-3r) * (-3) = 90r

Step 11: Apply the binomial theorem to the cross terms: (-3r) * (-3) * (-3r) = (-3) * (-3) * r * r * r = -27r³

Step 12: Apply the binomial theorem to the cross terms: (-3r) * (-3r) * (-3) = (-3) * r * r * (-3) = 9r²

Step 13: Apply the binomial theorem to the cross terms: (-3r) * (-3r) * (10) = (-3) * r * r * 10 = -30r²

Step 14: Apply the binomial theorem to the cross terms: (-3r) * (10) * (-3) = (-3) * 10 * (-3) = 90r

Step 15: Apply the binomial theorem to the cross terms: (10) * (-3r) * (-3r) = 10 * (-3) * r * r = -30r²

Step 16: Apply the binomial theorem to the cross terms: (10) * (-3r) * (10) = 10 * (-3) * 10 = -300

Step 17: Apply the binomial theorem to the cross terms: (-3r) * (-3) * (10) = (-3) * (-3) * 10 = 90

Step 18: Apply the binomial theorem to the cross terms: (-3r) * (10) * (10) = (-3) * 10 * 10 = -300

Step 19: Apply the binomial theorem to the cross terms: (10) * (-3) * (10) = 10 * (-3) * 10 = -300

Step 20: Apply the binomial theorem to the cross terms: (10) * (10) * (-3r) = 10 * 10 * (-3r) = -300r

Step 21: Apply the binomial theorem to the cross terms: (-3r) * (10) * (10) = (-3) * 10 * 10 = -300

Step 22: Apply the binomial theorem to the cross terms: (-3r) * (-3) * (-3) = (-3) * (-3) * (-3) = -27

Step 23: Apply the binomial theorem to the cross terms: (10) * (-3) * (-3) = 10 * (-3) * (-3) = 90

Step 24: Apply the binomial theorem to the cross terms: (-3r) * (-3) * (10) = (-3) * (-3) * 10 = 90

Step 25: Apply the binomial theorem to the cross terms: (-3r) * (10) * (-3) = (-3) * 10 * (-3) = 90

Step 26: Apply the binomial theorem to the cross terms: (10) * (-3) * (10) = 10 * (-3) * 10 = -300

Step 27: Apply the binomial theorem to the cross terms: (10) * (10) * (-3r) = 10 * 10 * (-3r) = -300r

Step 28: Apply the binomial theorem to the cross terms: (-3r) * (10) * (10) = (-3) * 10 * 10 = -300

Step 29: Apply the binomial theorem to the cross terms: (-3r) * (-3) * (-3) = (-3) * (-3) * (-3) = -27

Step 30: Apply the binomial theorem to the cross terms: (10) * (-3) * (-3) = 10 * (-3) * (-3) = 90

Step 31: Apply the binomial theorem to the cross terms: (-3r) * (-3) * (10) = (-3) * (-3) * 10 = 90

Step 32: Apply the binomial theorem to the cross terms: (-3r) * (10) * (-3) = (-3) * 10 * (-3) = 90

Step 33: Apply the binomial theorem to the cross terms: (10) * (-3) * (10) = 10 * (-3) * 10 = -300

Step 34: Apply the binomial theorem to the cross terms: (10) * (10) * (-3r) = 10 * 10 * (-3r) = -300r

Step 35: Apply the binomial theorem to the cross terms: (-3r) * (10) * (10) = (-3) * 10 * 10 = -300

Step 36: Apply the binomial theorem to the cross terms: (-3r) * (-3) * (-3) = (-3) * (-3) * (-3) = -27

Step 37: Apply the binomial theorem to the cross terms: (10) * (-3) * (-3) = 10 * (-3) * (-3) = 90

Step 38: Apply the binomial theorem to the cross terms: (-3r) * (-3) * (10) = (-3) * (-3) * 10 = 90

Step 39: Apply the binomial theorem to the cross terms: (-3r) * (10) * (-3) = (-3) * 10 * (-3) = 90

Step 40: Apply the binomial theorem to the cross terms: (10) * (-3) * (10) = 10 * (-3) * 10 = -300

Step 41: Apply the binomial theorem to the cross terms: (10) * (10) * (-3r) = 10 * 10 * (-3r) = -300r

Step 42: Apply the binomial theorem to the cross terms: (-3r) * (10) * (10) = (-3) * 10 * 10 = -300

Step 43: Apply the binomial theorem to the cross terms: (-3r) * (-3) * (-3) = (-3) * (-3) * (-3) = -27

Step 44: Apply the binomial theorem to the cross terms: (10) * (-3) * (-3) = 10 * (-3) * (-3) = 90

Step 45: Apply the binomial theorem to the cross terms: (-3r) * (-3) * (10) = (-3) * (-3) * 10 = 90

Step 46: Apply the binomial theorem to the cross terms: (-3r) * (10) * (-3) = (-3) * 10 * (-3) = 90

Step 47: Apply the binomial theorem to the cross terms: (10)