QuestionSubtract $-2 x^{2}+2$ from $-3 x^{2}+10$

Studdy Solution

STEP 1

What is this asking? We're taking one thing away from another thing, basically finding the difference between two mathematical expressions. Watch out! Subtracting a negative number is the same as adding a positive number!
Don't forget to distribute that minus sign correctly!

STEP 2

1. Set up the subtraction
2. Distribute the negative sign
3. Combine like terms

STEP 3

Alright, let's start by writing out the problem exactly as it's given to us.
We're subtracting $-2x^2 + 2$ from $-3x^2 + 10$ .
This translates to:
$(-3x^2 + 10) - (-2x^2 + 2)$

STEP 4

Remember, subtracting something is the same as adding its opposite!

STEP 5

Now, let's distribute that negative sign to each term in the second parentheses.
Think of it like multiplying each term by $-1$ .
$(-3x^2 + 10) + (2x^2 - 2)$

STEP 6

See how the signs flipped?
Subtracting a negative becomes adding a positive, and subtracting a positive becomes adding a negative!

STEP 7

Now comes the fun part!
Let's combine our like terms.
We've got $x^2$ terms and constant terms.

STEP 8

First, the $x^2$ terms: $-3x^2 + 2x^2 = (-3 + 2)x^2 = -1x^2 = -x^2$ .

STEP 9

Next, the constant terms: $10 - 2 = 8$ .

STEP 10

Putting it all together, we get $-x^2 + 8$ .
Boom!

STEP 11

Our final answer is $-x^2 + 8$ .

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