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

1: 64x4 - 400x3 + 719x2 - 300x + 31

2: 8x2 -25x +7

Explanation:

1: Using A=8x2 – 25x + 7, B=8x2– 25x + 11, C=10x2 – 25x + 7

Let's first compute A2:

A2 = (8x2 - 25x + 7)^2 = (8x2 - 25x + 7)*(8x2 - 25x + 7)

= 64x4 - 200x3 + 56x2 - 200x3 + 625x2 - 175x + 56x2 - 175x + 49

= 64x4 - 400x3 + 737x2 - 350x + 49

Now, let's compute (B + C):

B + C = 8x2– 25x + 11 + 10x2 – 25x + 7 = 18x2 - 50x + 18

Finally, we can do A2 - (B + C):

A2 - (B + C) = 64x4 - 400x3 + 737x2 - 350x + 49 - (18x2 - 50x + 18)

= 64x4 - 400x3 + 719x2 - 300x + 31

2: Using A = 3x – 4, B = x + 7, C = x2 + 2

A2 = (3x-4)^2 = (3x-4)*(3x-4) = 9x2 - 12x - 12x + 16 = 9x2 - 24x + 16

B + C = x + 7 + x2 + 2 = x2 + x + 9

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