Question

a43 - simplify like terms and the distributive pro
score: 3/13 answered: 3/13
question 4
combine all like terms in the proper order:
2 + 8 - 5 + 7x² - x² + 2 - 2x + 9x² - x - 7x²

Explanation:

Step1: Combine constant terms

First, we combine the constant terms (the terms without \(x\) or \(x^2\)): \(2 + 8 - 5 + 2\).
Calculating that: \(2 + 8 = 10\), \(10 - 5 = 5\), \(5 + 2 = 7\).

Step2: Combine \(x^2\) terms

Next, we combine the \(x^2\) terms: \(7x^2 - x^2 + 9x^2 - 7x^2\).
Using the distributive property (factoring out \(x^2\)): \((7 - 1 + 9 - 7)x^2\).
Calculating the coefficients: \(7 - 1 = 6\), \(6 + 9 = 15\), \(15 - 7 = 8\). So the \(x^2\) terms simplify to \(8x^2\).

Step3: Combine \(x\) terms

Then, we combine the \(x\) terms: \(-2x - x\).
Combining these: \((-2 - 1)x = -3x\).

Step4: Combine all simplified terms

Now, we combine the results from the previous steps: the constant term \(7\), the \(x^2\) term \(8x^2\), and the \(x\) term \(-3x\).
Putting them in standard form (descending powers of \(x\)): \(8x^2 - 3x + 7\).

Answer:

\(8x^2 - 3x + 7\)