If $$ A=m^{2}-9 m $$ and $$ B=1-9 m^{2} $$, find an expression that equals $$ 2 A-B $$ in standard form.

Question

UpStudy AI · Accepted Answer

To find an expression for $$ 2A - B $$ in standard form, follow these steps:

1. **Given Expressions:**
   $$
   A = m^2 - 9m
   $$
   $$
   B = 1 - 9m^2
   $$

2. **Calculate $$ 2A $$:**
   $$
   2A = 2(m^2 - 9m) = 2m^2 - 18m
   $$

3. **Subtract $$ B $$ from $$ 2A $$:**
   $$
   2A - B = (2m^2 - 18m) - (1 - 9m^2) = 2m^2 - 18m - 1 + 9m^2
   $$

4. **Combine like terms:**
   $$
   2A - B = (2m^2 + 9m^2) - 18m - 1 = 11m^2 - 18m - 1
   $$

5. **Standard Form:**
   The expression in standard form (arranged in descending powers of $$ m $$) is:
   $$
   11m^2 - 18m - 1
   $$

**Answer:**  
After simplifying, an equivalent standard form is 11 m² – 18 m – 1.
$$ 2A - B = 11m^2 - 18m - 1 $$

If \( A=m^{2}-9 m \) and \( B=1-9 m^{2} \), find an expression that equals \( 2 A-B \) in standard form.