Question

What is A2 – (B + C) in simplest form?

A=8x2 – 25x + 7
B=8x2– 25x + 11
C=10x2 – 25x + 7
D=10x2 – 25x + 11

A, B, and C are polynomials, where:
A = 3x – 4
B = x + 7
C = x2 + 2

Answer 1

Answer:
`8x^2 - 25x + 7`

Explanation:

Here,
`A = 3x - 4`,
`B = x + 7` and
`C = x^2 + 2`

`A^2 - (B + C)= (3x-4)^2-(x+7+x^2+2)` ( By putting the values)

=
`(3x)^2+ (4)^2- 2* 3x* 4- x- 7 - x^2 -2` ( solving the brackets)

=
`9x^2+ 16 - 24x - x- 7 - x^2 -2`

=
`8x^2- 25x + 7` ( By operating like terms)

⇒
`A^2 - (B + C) = 8x^2- 25x + 7`

Thus, Option A is correct.

Answer 2

A2 - (B + C) = (3x - 4)2 - ((x + 7)+ (x2 + 2))
A2 - (B + C) = 9x2 - 24x + 16 - (x2 + x + 9)
A2 - (B + C) = 9x2 - 24x + 16 - x2 - x - 9
A2 - (B + C) = 8x2 - 25x + 7

So, the answer is
A:
8x2 – 25x + 7