Question

If c(x)=a(x)+b(x), and a(x) and b(x) are give below, give the most simplified form of c(x). 1. a(x) = -2(x-5), b(x) = (4x+1)2

Answer 1

The most simplified form of c(x), where c(x) = a(x) + b(x), a(x) = -2(x-5), and b(x) = (4x+1)^2, is 16x^2 + 6x + 11.

To find the most simplified form of c(x), we need to combine a(x) and b(x) as stated in the equation c(x) = a(x) + b(x). First, we have:

a(x) = -2(x - 5)

Expand a(x):

-2 × x + 2 × 5 = -2x + 10

Then, we have:

b(x) = (4x + 1)2

Expand b(x) using the FOIL method:

(4x + 1)(4x + 1) = 16x2 + 4x + 4x + 1 = 16x2 + 8x + 1

Now add a(x) and b(x) to find c(x):

c(x) = (-2x + 10) + (16x2 + 8x + 1)

Combine like terms:

c(x) = 16x2 + 6x + 11

Therefore, the most simplified form of c(x) is 16x2 + 6x + 11.