What is the expansion of (4n - 3)^2?

What is the expansion of (4n - 3)^2?

• A. 16n^2 - 9
• B. 16n^2 - 24n + 9
• C. 16n^2 + 24n + 9
• D. 16n^2 - 12n + 9

Answer: (B)

To find the expansion of (4n - 3)², we can apply the formula for the square of a binomial, which is (a - b)² = a² - 2ab + b². In this case, a is 4n and b is 3. 1. First, calculate the square of the first term (4n): (4n)² = 16n². 2. Next, calculate the product of both terms multiplied by 2: 2 * (4n) * 3 = 24n. 3. Finally, calculate the square of the second term (3): 3² = 9. Now, we can combine these results according to the formula: (4n - 3)² = (4n)² - 2*(4n)*3 + 3², which simplifies to: 16n² - 24n + 9. Therefore, the correct expansion of (4n - 3)² is 16n² - 24n + 9. This aligns with the second choice provided.

To find the expansion of (4n - 3)², we can apply the formula for the square of a binomial, which is (a - b)² = a² - 2ab + b². In this case, a is 4n and b is 3.

1. First, calculate the square of the first term (4n):

(4n)² = 16n².

2. Next, calculate the product of both terms multiplied by 2:

2 * (4n) * 3 = 24n.

3. Finally, calculate the square of the second term (3):

3² = 9.

Now, we can combine these results according to the formula:

(4n - 3)² = (4n)² - 2*(4n)*3 + 3²,

which simplifies to:

16n² - 24n + 9.

Therefore, the correct expansion of (4n - 3)² is 16n² - 24n + 9. This aligns with the second choice provided.