Question

1. $(2x^2 - 5x) - 2(x^2 + 10x - 3)$; $-2x^2 - 20x + 6$

Explanation:

Step1: Distribute the -2

Multiply -2 with each term inside the parentheses: \(-2(x^2 + 10x - 3) = -2x^2 - 20x + 6\)

Step2: Combine with the first part

Now we have \((2x^2 - 5x) + (-2x^2 - 20x + 6)\). Combine like terms:

• For \(x^2\) terms: \(2x^2 - 2x^2 = 0\)
• For \(x\) terms: \(-5x - 20x = -25x\)
• Constant term: \(+6\)

So the simplified expression is \(-25x + 6\) (Wait, but let's check again. Wait, the original first part is \((2x^2 - 5x)\) and then we have \(-2(x^2 + 10x - 3)\). Wait, maybe I misread. Wait, the problem as written: \((2x^2 - 5x) - 2(x^2 + 10x - 3)\). Wait, when we distribute -2: \(-2x^2 -20x +6\). Then add to \(2x^2 -5x\): \(2x^2 -5x -2x^2 -20x +6\). Now combine like terms: \(2x^2 -2x^2 = 0\), \(-5x -20x = -25x\), and +6. So the result is \(-25x + 6\). But the colored parts show \(-2x^2 -20x +6\) which is the distributed part, then we need to add the first part. Wait, maybe the problem was to just distribute the -2, but the final step is to combine. Wait, let's re-express.

Wait, maybe the original problem was to expand \(-2(x^2 + 10x - 3)\) which gives \(-2x^2 -20x +6\), and then if we combine with \((2x^2 -5x)\), the full simplification is:

\(2x^2 -5x -2x^2 -20x +6 = (2x^2 -2x^2) + (-5x -20x) +6 = -25x +6\)

But if the task was just to distribute the -2, then the distributed form is \(-2x^2 -20x +6\), and then combining with the first polynomial gives the simplified form.

Answer:

If simplifying the entire expression \((2x^2 - 5x) - 2(x^2 + 10x - 3)\), the answer is \(-25x + 6\). If the task was to distribute the -2, the distributed part is \(-2x^2 - 20x + 6\), and then combining with the first polynomial gives \(-25x + 6\).