If B, equals, 3, x, minus, x, squaredB=3x−x

Question

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:

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