Arrange 5a+a²+3-7+a+a² in the descending powers of a

To arrange the expression \( 5a + a^2 + 3 - 7 + a + a^2 \) in descending powers of \( a \):

1. **Combine like terms**:
   - The terms with \( a^2 \) are \( a^2 + a^2 \) which sum up to \( 2a^2 \).
   - The terms with \( a \) are \( 5a + a \) which sum up to \( 6a \).
   - The constant terms are \( 3 - 7 \) which sum up to \( -4 \).

2. **Write the expression in descending order**:
   \[
   2a^2 + 6a - 4
   \]

So, the expression arranged in descending powers of \( a \) is \( 2a^2 + 6a - 4 \).

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you factor the expression \( 2a^2 + 6a - 4 \)?
2. What are the roots of the equation \( 2a^2 + 6a - 4 = 0 \)?
3. How would the expression change if \( a \) were negative?
4. What is the vertex form of the quadratic expression \( 2a^2 + 6a - 4 \)?
5. How does the coefficient of \( a^2 \) affect the shape of its graph?

**Tip:** Always combine like terms first when simplifying expressions to make further calculations easier.

Learn how to arrange the expression 5a + a^2 + 3 - 7 + a + a^2 in descending powers of a. This problem involves combining like terms and organizing the expression in a structured form. Suitable for students in Grades 7-9 studying algebra and quadratic equations.

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