Writing as a simplified polynomial in standard form, what is the result when (2x+3)^2 is subtracted from 8x^2-8x-9?

Answer 1

To find the result when $(2x+3)^2$ is subtracted from $8x^2-8x-9$, we first need to expand $(2x+3)^2$.

Using the formula $(a+b)^2 = a^2 + 2ab + b^2$, where $a = 2x$ and $b = 3$, we have:

$(2x+3)^2 = (2x)^2 + 2(2x)(3) + (3)^2$
$= 4x^2 + 12x + 9$

Now, subtract this from $8x^2-8x-9$:

$(8x^2-8x-9) - (4x^2 + 12x + 9)$
$= 8x^2 - 8x - 9 - 4x^2 - 12x - 9$
$= (8x^2 - 4x^2) + (-8x - 12x) + (-9 - 9)$
$= 4x^2 - 20x - 18$

Therefore, the result when $(2x+3)^2$ is subtracted from $8x^2-8x-9$ is $4x^2 - 20x - 18$.