Question

Fill in the parts-whole model for the following equation.
left parenthesis, minus, 10, x, squared, minus, 5, x, plus, 6, right parenthesis, plus, left parenthesis, minus, 5, x, squared, plus, 8, right parenthesis, equals, left parenthesis, start underline, end underline, right parenthesis
(−10x
2
−5x+6)+(−5x
2
+8)=(
​
)

Answer 1

To fill in the parts-whole model for the equation \((−10x^2 − 5x + 6) + (−5x^2 + 8) = (\underline{\ \ \ })\), we first need to simplify the left side of the equation by combining like terms.

1. **Combine the \(x^2\) terms:**
\[
-10x^2 - 5x^2 = -15x^2
\]

2. **Combine the \(x\) terms:**
\[
-5x \text{ (there is no other \(x\) term to combine)}
\]

3. **Combine the constant terms:**
\[
6 + 8 = 14
\]

Now, we can write the simplified expression:
\[
-15x^2 - 5x + 14
\]

Therefore, the completed parts-whole model is:
\[
(−10x^2 − 5x + 6) + (−5x^2 + 8) = (−15x^2 − 5x + 14)
\]

The final answer to fill in the blank is:
\[
−15x^2 − 5x + 14
\]