Question

Subtract: 3x to the power 2 - 6x - 4 from 5 + x - 2xto the power 2.

Answer 1

`-8x^2 - 4x + 29 \\`

Explanation:

Second expression evaluates to:

`(5 + x -2x)^2 = (5 -x)^2 = (-x+5)^2 = x^2 + 2(-x)(5) +5^2 = x^2 -10x + 25` (1)

For (1) We are using the rule
`(a+b)^2 = a^2 +2ab + b^2\\\\`

Here
`a = -x, b = 5\\\\`

First expression evaluates to

`(3x)^2 -6x - 4 = 9x^2 -6x -4` (2)

Subtract (2) from (1)

`x^2 - 10x +25 - (9x^2 -6x -4) = x^2-9x^2 -10x - (-6x) +25 -(-4)\\\\= -8x^2 - 4x + 29 \\`