Question

fill in the parts-whole model for the following equation.
(____) = (-10x² - 5x + 7) + (-8x² + 3x + 6)

Explanation:

Step1: Combine like terms for \(x^2\)

We have \(-10x^2\) and \(-8x^2\). Adding them together: \(-10x^2 + (-8x^2) = -18x^2\)

Step2: Combine like terms for \(x\)

We have \(-5x\) and \(3x\). Adding them together: \(-5x + 3x = -2x\)

Step3: Combine constant terms

We have \(7\) and \(6\). Adding them together: \(7 + 6 = 13\)

Step4: Combine all combined terms

Now, combine the results from Step1, Step2, and Step3: \(-18x^2 - 2x + 13\)

The two parts (the two polynomials being added) are \(-10x^2 - 5x + 7\) and \(-8x^2 + 3x + 6\), and the whole (the sum) is \(-18x^2 - 2x + 13\).

Answer:

The whole (the left - hand side of the equation) is \(\boldsymbol{-18x^2 - 2x + 13}\). The two parts (the right - hand side polynomials) are \(\boldsymbol{-10x^2 - 5x + 7}\) and \(\boldsymbol{-8x^2 + 3x + 6}\) (for the parts - whole model, the top box is the whole \(-18x^2 - 2x + 13\) and the bottom two boxes are \(-10x^2 - 5x + 7\) and \(-8x^2 + 3x + 6\) respectively).