Question

Fill in the parts-whole model for the following equation.
left parenthesis, minus, x, squared, minus, x, plus, 8, right parenthesis, minus, left parenthesis, 5, x, squared, minus, 8, x, plus, 3, right parenthesis, equals, left parenthesis, start underline, end underline, right parenthesis
(−x
2
−x+8)−(5x
2
−8x+3)=(
​
)

Answer 1

To fill in the parts-whole model for the equation

\[
(-x^2 - x + 8) - (5x^2 - 8x + 3) = ( \, \underline{ } \, )
\]

we need to simplify the left-hand side of the equation by combining like terms.

1. Rewrite the equation:
\[
-x^2 - x + 8 - (5x^2 - 8x + 3)
\]

2. Distribute the negative sign across the second parentheses:
\[
-x^2 - x + 8 - 5x^2 + 8x - 3
\]

3. Combine like terms:
- The \(x^2\) terms: \(-x^2 - 5x^2 = -6x^2\)
- The \(x\) terms: \(-x + 8x = 7x\)
- The constant terms: \(8 - 3 = 5\)

4. Combine everything:
\[
-6x^2 + 7x + 5
\]

Now we have simplified the expression:

\[
(-x^2 - x + 8) - (5x^2 - 8x + 3) = -6x^2 + 7x + 5
\]

So we can fill in the parts-whole model:

\[
\underline{-6x^2 + 7x + 5}
\]

Final answer:

\[
(-x^2 - x + 8) - (5x^2 - 8x + 3) = \underline{-6x^2 + 7x + 5}
\]