Question

When (2x - 3)² is written in the form ax² + bx +c, where a, b, and c are integers, a +b+c =?

a) -17
b) -5
c) 13
d) 25

Answer 1

When expanding (2x - 3)², we obtain 4x² - 12x + 9. Hence, a = 4, b = -12, and c = 9. Adding a, b, and c together gives us a result of 1, which is not an option in the multiple choices provided.

Step-by-step explanation:

To expand (2x - 3)² we can use the formula (a - b)² = a² - 2ab + b². Following this pattern:

• a = 2x, so a² = (2x)² = 4x²
• b = 3, so b² = 3² = 9
• And 2ab = 2(2x)(3) = 12x

Now, we can put these together:

(2x - 3)² = 4x² - 12x + 9

Therefore, a = 4, b = -12, and c = 9. To find a + b + c, we just sum these numbers:

4 - 12 + 9 = 1

Thus, the answer to the student's question is that a + b + c equals 1, which is not listed among the provided options, suggesting there might be a mistake in the options given.