Question

Fill in the parts-whole model for the following equation.
left parenthesis, 8, x, squared, minus, 8, x, minus, 13, right parenthesis, minus, left parenthesis, start underline, end underline, right parenthesis, equals, 7, x, squared, minus, 7, x, minus, 7
(8x
2
−8x−13)−(
​
)=7x
2
−7x−7

Answer 1

To fill in the parts-whole model for the given equation, we need to identify what part is being subtracted from the whole to equal the specified result.

The equation can be rewritten for clarity:

\[
(8x^2 - 8x - 13) - ( \text{?} ) = (7x^2 - 7x - 7)
\]

We want to find what is being subtracted (let's denote it as \(A\)):

\[
A = (8x^2 - 8x - 13) - (7x^2 - 7x - 7)
\]

Now, let's simplify:

\[
A = 8x^2 - 8x - 13 - 7x^2 + 7x + 7
\]

Combine like terms:

1. Combine \(8x^2\) and \(-7x^2\):
\[
8x^2 - 7x^2 = 1x^2 = x^2
\]

2. Combine \(-8x\) and \(7x\):
\[
-8x + 7x = -1x = -x
\]

3. Combine \(-13\) and \(+7\):
\[
-13 + 7 = -6
\]

Putting it all together, we find:
\[
A = x^2 - x - 6
\]

So we can complete the parts-whole model:

\[
(8x^2 - 8x - 13) - (x^2 - x - 6) = 7x^2 - 7x - 7
\]

Thus, the answer to fill in the underline is:

\[
x^2 - x - 6
\]