Question

Q7 According to the Distributive Property which expression is equivalent to 5x2+10x+15?
5(x2+2x+3)
5(x2+10x+3)
5(x2+10x+15)
x(5x+10+15)

Answer 1

Q8 Simplify the expression 3x^2-2x^2+4x-6

Answer 2

Q9 Add the polynomial expressions 3y-4y2+7y+2 and 5y2+6-8y.

Answer 3

To find the expression that is equivalent to \(5x^2 + 10x + 15\) using the Distributive Property, we can factor out the common factor, which is 5.

Starting from the original expression:

\[
5x^2 + 10x + 15
\]

We can factor out 5:

\[
5(x^2 + 2x + 3)
\]

Thus, the equivalent expression is:

\[
5(x^2 + 2x + 3)
\]

Among the options provided, the correct choice is:

**5(x^2 + 2x + 3)**.

Answer 4

To simplify the expression \(3x^2 - 2x^2 + 4x - 6\), we can combine like terms.

1. Combine the \(x^2\) terms:
\[
3x^2 - 2x^2 = (3 - 2)x^2 = 1x^2 = x^2
\]

2. The \(4x\) term remains the same, as there are no other \(x\) terms to combine with it:
\[
4x
\]

3. The constant term \(-6\) also remains unchanged.

Putting it all together, we have:
\[
x^2 + 4x - 6
\]

Thus, the simplified expression is:
\[
\boxed{x^2 + 4x - 6}
\]

Answer 5

To add the polynomial expressions \(3y - 4y^2 + 7y + 2\) and \(5y^2 + 6 - 8y\), we will first combine like terms.

1. **First Polynomial**: \(3y - 4y^2 + 7y + 2\)
- Combine the \(y\) terms:
\[
3y + 7y = 10y
\]
- The polynomial becomes:
\[
-4y^2 + 10y + 2
\]

2. **Second Polynomial**: \(5y^2 + 6 - 8y\)
- Rearranging gives:
\[
5y^2 - 8y + 6
\]

Now, we'll add the two simplified polynomials together:

\[
(-4y^2 + 10y + 2) + (5y^2 - 8y + 6)
\]

Combine the like terms:

- **\(y^2\) terms**:
\[
-4y^2 + 5y^2 = 1y^2 = y^2
\]

- **\(y\) terms**:
\[
10y - 8y = 2y
\]

- **Constant terms**:
\[
2 + 6 = 8
\]

Putting it all together, we get:

\[
y^2 + 2y + 8
\]

Thus, the sum of the polynomials is:

\[
\boxed{y^2 + 2y + 8}
\]