Question

If B, equals, 3, x, minus, x, squaredB=3x−x
2
and C, equals, x, minus, 8, minus, 8, x, squared, commaC=x−8−8x
2
, find an expression that equals 2, B, minus, 2, C2B−2C in standard form.

Answer 1

To find the expression \( 2B - 2C \) in standard form given

\[
B = 3x - x^2 \quad \text{and} \quad C = x - 8 - 8x^2
\]

we will first calculate \( 2B \) and \( 2C \).

1. **Calculate \( 2B \)**:

\[
2B = 2(3x - x^2) = 6x - 2x^2
\]

2. **Calculate \( 2C \)**:

\[
2C = 2(x - 8 - 8x^2) = 2x - 16 - 16x^2
\]

3. **Now, find \( 2B - 2C \)**:

\[
2B - 2C = (6x - 2x^2) - (2x - 16 - 16x^2)
\]

We distribute the negative sign through \( 2C \):

\[
= 6x - 2x^2 - 2x + 16 + 16x^2
\]

Now, combine like terms:

- For \( x \) terms: \( 6x - 2x = 4x \)
- For \( x^2 \) terms: \( -2x^2 + 16x^2 = 14x^2 \)

Thus, we have:

\[
2B - 2C = 14x^2 + 4x + 16
\]

4. **Standard form**:

The standard form of a polynomial is typically expressed in descending order of the powers of \( x \). Putting it all together, we express \( 2B - 2C \) as:

\[
\boxed{14x^2 + 4x + 16}
\]