Question

a, b, and c are polynomials, where: a = 3x - 4, b = x + 7, c = x² + 2. what is a² - (b + c) in simplest form? options: 8x² - 25x + 7, 8x² - 25x + 11, 10x² - 25x + 7, 10x² - 25x + 11

Explanation:

Step1: Calculate $A^2$

$$(3x-4)^2 = 9x^2 - 24x + 16$$

Step2: Calculate $B+C$

$$(x+7)+(x^2+2) = x^2 + x + 9$$

Step3: Subtract $B+C$ from $A^2$

$$(9x^2 - 24x + 16) - (x^2 + x + 9) = 9x^2 -24x +16 -x^2 -x -9$$

Step4: Combine like terms

$$(9x^2 -x^2) + (-24x -x) + (16-9) = 8x^2 -25x +7$$

Answer:

○ $8x^2 -25x +7$