Question

What is the standard form of `y= (2x-9)(x-5)-(2x+7)^2`?

Answer 1

`y=-2x^2-47x-4`

Explanation:

The general standard form for a quadratic is
`color(white)("XXX")y=ax^2+bx+c`
with constants `a, b, c`

Given
`color(white)("XXX")y=color(red)((2x-9)(x-5))-color(blue)((2x+7)^2)`

Expanding the terms:
`color(white)("XXX")y=color(red)((2x^2-19x+45))-color(blue)((4x^2+28x+49))`

Combine like terms:
`color(white)("XXX")y=-2x^2-47x-4`