To find the difference between the given expressions [tex]\(2a^2 - 3a\)[/tex] and [tex]\(-4a^2 + 7\)[/tex], follow these steps:
1. Write the difference expression:
[tex]\[
\left(2a^2 - 3a\right) - \left(-4a^2 + 7\right)
\][/tex]
2. Distribute the negative sign through the second expression:
Since we are subtracting the entire second expression, distribute the negative sign:
[tex]\[
\left(2a^2 - 3a\right) + \left(4a^2 - 7\right)
\][/tex]
3. Combine like terms:
- Combine the [tex]\(a^2\)[/tex] terms: [tex]\(2a^2 + 4a^2 = 6a^2\)[/tex]
- Combine the [tex]\(a\)[/tex] terms: [tex]\(-3a + 0 = -3a\)[/tex]
- Combine the constant terms: [tex]\(0 - 7 = -7\)[/tex]
4. Write the simplified expression:
[tex]\[
6a^2 - 3a - 7
\][/tex]
So, the difference between the expressions [tex]\( \left(2a^2 - 3a\right) \)[/tex] and [tex]\( \left(-4a^2 + 7\right) \)[/tex] is:
[tex]\[
6a^2 - 3a - 7
\][/tex]
