Fill in the parts-whole model for the following equation.

Question

left parenthesis, 3, x, squared, minus, 17, x, minus, 2, right parenthesis, minus, left parenthesis, start underline, end underline, right parenthesis, equals, 10, x, squared, minus, 10, x, minus, 3
(3x
2
−17x−2)−(
​
)=10x
2
−10x−3

Answer 1

To fill in the parts-whole model for the equation

\[ (3x^2 - 17x - 2) - (\underline{\quad}) = 10x^2 - 10x - 3, \]

we need to determine what the missing term (the subtracted expression) is that, when subtracted from \(3x^2 - 17x - 2\), will yield \(10x^2 - 10x - 3\).

Let's denote the missing expression as \(E\). We can rewrite the equation as:

\[ E = (3x^2 - 17x - 2) - (10x^2 - 10x - 3). \]

Now, we'll simplify the right-hand side by distributing the negative sign:

\[ E = 3x^2 - 17x - 2 - 10x^2 + 10x + 3. \]

Now, let's combine like terms:

1. Combine \(3x^2\) and \(-10x^2\):

\[ 3x^2 - 10x^2 = -7x^2. \]

2. Combine \(-17x\) and \(10x\):

\[ -17x + 10x = -7x. \]

3. Combine \(-2\) and \(3\):

\[ -2 + 3 = 1. \]

Now, putting it all together, we get:

\[ E = -7x^2 - 7x + 1. \]

So the completed equation is:

\[ (3x^2 - 17x - 2) - (-7x^2 - 7x + 1) = 10x^2 - 10x - 3. \]

Thus, the part to fill in the blanks is

\[ \underline{-7x^2 - 7x + 1}. \]