If $$ B=1-6 w^{2} $$ and $$ A=1+w $$, find an expression that equals $$ 2 B-A $$ in standard form. Answer Attempt 1 out of 2

Question

UpStudy AI · Accepted Answer

To find the expression that equals $$ 2B - A $$, we will first substitute the expressions for $$ B $$ and $$ A $$ into the equation.

1. **Substituting the expressions:**
   - We have $$ B = 1 - 6w^2 $$ and $$ A = 1 + w $$.
   - Therefore, $$ 2B = 2(1 - 6w^2) $$ and $$ A = 1 + w $$.

2. **Calculating $$ 2B $$:**
   $$
   2B = 2(1 - 6w^2) = 2 - 12w^2
   $$

3. **Now, substituting into $$ 2B - A $$:**
   $$
   2B - A = (2 - 12w^2) - (1 + w)
   $$

4. **Distributing the negative sign:**
   $$
   2B - A = 2 - 12w^2 - 1 - w
   $$

5. **Combining like terms:**
   $$
   2B - A = (2 - 1) - w - 12w^2 = 1 - w - 12w^2
   $$

Now, we have the expression in standard form:
$$
2B - A = -12w^2 - w + 1
$$

Thus, the final expression that equals $$ 2B - A $$ in standard form is:
$$
-12w^2 - w + 1
$$
$$ 2B - A = -12w^2 - w + 1 $$

If \( B=1-6 w^{2} \) and \( A=1+w \), find an expression that equals \( 2 B-A \) in standard form. Answer Attempt 1 out of 2