Math  /  Algebra

Question12. [-/1 Points]
DETAILS MY NOTES EWENMATH12 5.2.050. Simplify by first removing the parentheses and then combining the like terms. (2x+4)(x6)(2 x+4)-(x-6) \square Need Help? Read It

Studdy Solution

STEP 1

What is this asking? Simplify the expression by getting rid of the parentheses and then grouping similar terms. Watch out! Be super careful with the signs when removing the parentheses, especially when subtracting!

STEP 2

1. Remove parentheses
2. Combine like terms

STEP 3

Alright, let's **get rid of those parentheses**!
We have (2x+4)(x6)(2x + 4) - (x - 6).
Remember, subtracting a quantity is the same as adding its opposite.
So, subtracting (x6)(x - 6) is the same as adding (x+6)(-x + 6).

STEP 4

So, our expression becomes 2x+4+(x+6)2x + 4 + (-x + 6).
Notice how the sign of each term inside the second parentheses flipped!
That's because we were subtracting!

STEP 5

Now, let's **group the terms with** xx **together** and the **constant terms together**.
We have 2x2x, and x-x for the xx terms.
For the constants, we have 44 and 66.

STEP 6

Combining the xx terms, we have 2x+(x)=(21)x=1x=x2x + (-x) = (2-1) \cdot x = 1 \cdot x = x.
Remember, 2x2x means we have two "x's", and x-x means we take away one "x".
So we're left with one xx, which we just write as xx.

STEP 7

Combining the constant terms, we have 4+6=104 + 6 = 10.
Easy peasy!

STEP 8

Putting it all together, our simplified expression is x+10x + 10!

STEP 9

x+10x + 10

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord