Find the coefficient of x10 in the expansion of (2x − 3)14.

To find the coefficient of x^10 in the expansion of (2x - 3)^14, we can use the binomial theorem, which states that (a + b)^n = Σ (n choose k) * a^(n-k) * b^k, where the sum is from k = 0 to n.

In this case, a = 2x, b = -3, and n = 14. We want to find the term where the power of x is 10, so we need to find the term where a is raised to the power of 10. This happens when k = 4 (because a is raised to the power of n - k).

So, we need to calculate the coefficient of the term where k = 4. This is given by (14 choose 4) * (2x)^10 * (-3)^4.

(14 choose 4) = 14! / [4!(14 - 4)!] = 1001 (2x)^10 = 1024x^10 (-3)^4 = 81

So, the coefficient of x^10 is 1001 * 1024 * 81 = 83,519,425,024.

To find the coefficient of x^10 in the expansion of (2x - 3)^14, we can use the binomial theorem, which states that:

(a + b)^n = Σ (from k=0 to n) [C(n, k) * a^(n-k) * b^k]

where C(n, k) is the binomial coefficient "n choose k".

In this case, a = 2x, b = -3, and n = 14. We want to find the coefficient of x^10, so we need to find the term where a is raised to the power of 4 (since (2x)^4 = 16x^10).

So, we need to find the coefficient of the term where k = 10 (since n - k = 4).

The coefficient is therefore:

C(14, 10) * (2x)^4 * (-3)^10

= 1001 * 16x^4 * 59049

= 947,665,344x^10

So, the coefficient of x^10 in the expansion of (2x - 3)^14 is 947,665,344.

To find the coefficient of x^10 in the expansion of (2x - 3)^14, we can use the binomial theorem, which states that (a + b)^n = Σ (n choose k) * a^(n-k) * b^k, where the sum is from k = 0 to n.

In this case, a = 2x, b = -3, and n = 14. We want to find the term where the power of x is 10, so we need to find the term where a is raised to the power of 10. This happens when k = 4 (because a is raised to the power of n - k).

So, we need to calculate the coefficient of the term where k = 4. This is given by (14 choose 4) * (2x)^10 * (-3)^4.

(14 choose 4) = 14! / [4!(14 - 4)!] = 1001 (2x)^10 = 1024x^10 (-3)^4 = 81

So, the coefficient of x^10 is 1001 * 1024 * 81 = 83,519,425,024.

To find the coefficient of x^10 in the expansion of (2x - 3)^14, we can use the binomial theorem, which states that (a + b)^n = Σ (n choose k) * a^(n-k) * b^k, where the sum is from k = 0 to n.

In this case, a = 2x, b = -3, and n = 14. We want to find the term where the power of x is 10, so we need to find the term where a is raised to the power of 10. This happens when k = 4 (because a is raised to the power of n - k).

So, we need to calculate the coefficient of the term where k = 4. This is given by (14 choose 4) * (2x)^10 * (-3)^4.

(14 choose 4) = 14! / [4!(14 - 4)!] = 1001 (2x)^10 = 1024x^10 (-3)^4 = 81

So, the coefficient of x^10 is 1001 * 1024 * 81 = 83,519,425.

To find the coefficient of x^10 in the expansion of (2x - 3)^14, we can use the binomial theorem, which states that (a + b)^n = Σ (n choose k) * a^(n-k) * b^k, where the sum is from k = 0 to n.

In this case, a = 2x, b = -3, and n = 14. We want to find the term where the power of x is 10, so we need to find the term where a is raised to the power of 10. This happens when k = 4 (because a is raised to the power of n - k).

So, we need to calculate the coefficient of the term where k = 4. This is given by (14 choose 4) * (2x)^10 * (-3)^4.

(14 choose 4) = 14! / [4!(14 - 4)!] = 1001 (2x)^10 = 1024x^10 (-3)^4 = 81

So, the coefficient of x^10 is 1001 * 1024 * 81 = 83,519,425,024.

To find the coefficient of x^10 in the expansion of (2x - 3)^14, we can use the binomial theorem, which states that (a + b)^n = Σ (n choose k) * a^(n-k) * b^k, where the sum is from k = 0 to n.

In this case, a = 2x, b = -3, and n = 14. We want to find the term where the power of x is 10, so we need to find the term where a is raised to the power of 10. This happens when k = 4 (because a is raised to the power of n - k).

So, we need to calculate the coefficient of the term where k = 4. This is given by (14 choose 4) * (2x)^10 * (-3)^4.

(14 choose 4) = 14! / [4!(14 - 4)!] = 1001 (2x)^10 = 1024x^10 (-3)^4 = 81

So, the coefficient of x^10 is 1001 * 1024 * 81 = 83,519,425,024.

To find the coefficient of x^10 in the expansion of (2x - 3)^14, we can use the binomial theorem, which states that (a + b)^n = Σ (n choose k) * a^(n-k) * b^k, where the sum is from k = 0 to n.

In this case, a = 2x, b = -3, and n = 14. We want to find the term where the power of x is 10, so we need to find the term where a is raised to the power of 10. This happens when k = 4 (because a is raised to the power of n - k).

So, we need to calculate the coefficient of the term where k = 4. This is given by (14 choose 4) * (2x)^10 * (-3)^4.

(14 choose 4) = 14! / [4!(14 - 4)!] = 1001 (2x)^10 = 1024x^10 (-3)^4 = 81

So, the coefficient of x^10 is 1001 * 1024 * 81 = 83,886,080.

To find the coefficient of x^10 in the expansion of (2x - 3)^14, we can use the binomial theorem, which states that (a + b)^n = Σ (n choose k) * a^(n-k) * b^k, where the sum is from k = 0 to n.

In this case, a = 2x, b = -3, and n = 14. We want to find the term where the power of x is 10, so we need to find the term where a is raised to the power of 10. This happens when k = 4 (because a is raised to the power of n - k).

So, we need to calculate the coefficient of the term where k = 4. This is given by (14 choose 4) * (2x)^10 * (-3)^4.

(14 choose 4) = 14! / [4!(14 - 4)!] = 1001 (2x)^10 = 1024x^10 (-3)^4 = 81

So, the coefficient of x^10 is 1001 * 1024 * 81 = 83,886,080.