Question

Fill in the blanks with the correct coefficients when simplifying the expression.(14x+6y)+(5x+12y) x+y

Answer 1

To simplify the expression \((14x + 6y) + (5x + 12y)(x + y)\), we first need to perform the multiplication and then add the like terms.

1. **Multiply \((5x + 12y)\) and \((x + y)\)**:
\[
(5x + 12y)(x + y) = 5x \cdot x + 5x \cdot y + 12y \cdot x + 12y \cdot y
\]
This results in:
\[
5x^2 + 5xy + 12xy + 12y^2
\]
Combining the like terms \(5xy + 12xy\):
\[
5x^2 + 17xy + 12y^2
\]

2. **Now substitute this back into the original expression**:
\[
(14x + 6y) + (5x^2 + 17xy + 12y^2)
\]

3. **Combine all terms**:
\[
5x^2 + 14x + 17xy + 6y + 12y^2
\]

Putting it all together, the expression simplifies to:
\[
5x^2 + 14x + 17xy + 12y^2 + 6y
\]

In this expression:
- The coefficient of \(x^2\) is **5**,
- The coefficient of \(x\) is **14**,
- The coefficient of \(xy\) is **17**,
- The coefficient of \(y\) is **6**,
- The coefficient of \(y^2\) is **12**.

Thus, the correct coefficients are:
- \(5\) for \(x^2\)
- \(14\) for \(x\)
- \(17\) for \(xy\)
- \(6\) for \(y\)
- \(12\) for \(y^2\)