Question

given the quadratic below, determine the values of a, b, and c. select all correct answers.
$(4x - 5)^2 = ax^2 + bx + c$
□ a=8
□ a=16
□ b=0
□ b=-40
□ b=40
□ c=25
□ c=-25

Explanation:

Step1: Expand the left - hand side

We use the formula \((a - b)^2=a^{2}-2ab + b^{2}\), where \(a = 4x\) and \(b = 5\).
\((4x-5)^{2}=(4x)^{2}-2\times(4x)\times5 + 5^{2}\)
\(=16x^{2}-40x + 25\)

Step2: Compare with \(ax^{2}+bx + c\)

By comparing \(16x^{2}-40x + 25\) with \(ax^{2}+bx + c\), we can see that:

• For the coefficient of \(x^{2}\): \(a = 16\)
• For the coefficient of \(x\): \(b=-40\)
• For the constant term: \(c = 25\)

Answer:

a = 16, b=-40, c = 25 (So the correct options are: a = 16, b=-40, c = 25)