Step by step
Distribute the −2
In the warm-up, 4x − 2(3x − 5) + 7x − 9, multiply the −2 into (3x − 5): −2 × 3x = −6x and −2 × −5 = +10. Then rewrite everything else as it was.
▶ Watch this step 0:12Combine the warm-up's like terms
The x terms are 4x, −6x and 7x. Mr DJ adds 4x + 7x = 11x first, then 11x − 6x = 5x. The numbers are +10 − 9 = +1, so the warm-up simplifies to 5x + 1.
▶ Watch this step 0:35Distribute the 5
In the main problem, multiply the 5 by every term in (2x² − 3x + 4): 5 × 2x² = 10x², 5 × −3x = −15x and 5 × 4 = +20.
▶ Watch this step 1:11Distribute the −3
Next, −3 × x² = −3x² and −3 × −5x = +15x, since a negative times a negative is positive. The rest stays the same: + 4x² − 12 − 8x.
▶ Watch this step 1:28Group like terms by color
Mr DJ marks the x² terms (10x², −3x², +4x²) in green and the x terms (−15x, +15x, −8x) in orange. The last group is the numbers, +20 and −12.
▶ Watch this step 1:51Combine the numbers
He starts with the numbers: +20 − 12 = +8. Then he moves on to the x terms and the x² terms.
▶ Watch this step 2:16Combine the x terms
−15x and +15x cancel each other out. Is there any other orange term? Yes, −8x, so that's what's left.
▶ Watch this step 2:27Combine the x² terms
10x² − 3x² = 7x², and 7x² + 4x² = 11x². Put the three groups together: 11x² − 8x + 8.
▶ Watch this step 2:41
Worked example · with Digit the Fox
Try one more, step by step
Problem: Simplify 4(x² − 2x + 3) − 2(3x² − 4x) + 5x² − 9 + 2x
- Distribute the 4: 4x² − 8x + 12
- Distribute the −2: −2 × 3x² = −6x² and −2 × −4x = +8x
- Rewrite: 4x² − 8x + 12 − 6x² + 8x + 5x² − 9 + 2x
- Group: x² terms 4x², −6x², +5x²; x terms −8x, +8x, +2x; numbers +12, −9
- Numbers: 12 − 9 = +3
- x terms: −8x and +8x cancel, leaving +2x
- x² terms: 4x² − 6x² = −2x², then −2x² + 5x² = 3x²
Answer: 3x² + 2x + 3
Check: Try x = 1: the original gives 4(2) − 2(−1) + 5 − 9 + 2 = 8, and 3 + 2 + 3 = 8.
Common mistakes
- Multiplying only the first term: 5(2x² − 3x + 4) becomes 10x² − 3x + 4. Multiply the 5 by every term inside: 10x² − 15x + 20.
- Losing a sign: writing −3 × −5x as −15x. A negative times a negative is positive, so −3 × −5x = +15x.
- Combining x² terms with x terms, like turning 10x² − 15x into −5x. x² and x are not like terms. Keep them in separate color groups.
- Forgetting a leftover term after a pair cancels, like dropping the −8x after −15x + 15x = 0. After a pair cancels, check that group again. Mr DJ asks if there's any other orange term and finds the −8x.
Questions
What are like terms?
Like terms have the same variable part, so they can be combined. Here the x² terms go together, the x terms go together and the plain numbers go together, and Mr DJ keeps track of them with colors.
Do you distribute before combining like terms?
Yes. In both problems Mr DJ distributes first: −2(3x − 5) becomes −6x + 10, and only then does he combine it with the other x terms and numbers.
Read the full transcript
0:00 This is just a warm-up problem. Stick around for the final boss. 2 minutes to solve this combining like terms problem. Here we go. Let's get started. Okay, I'm going to distribute this -2 into the parentheses. So, -2 × +3x gets me -6x. And distribute the -2 to the -5 gets me +10. Okay, we did distributive property. Let's rewrite everything else. Okay. Next, let's take a look here. Let's um let's combine all the like terms. So, we have a 4x -6x and a positive 6x. Okay, so the 4x and the 7x get us 11x.
0:47 Right? So, we can combine those. We'll just say 11x. We have -6x +10 -9 and then we have the 11x -6x is 5x plus Let me combine these to get +1. And that's it. Okay, here we go. 5 × 2x squared gets us 10 x squared. 5 × a -3x is - 15x. 5 * 4 is + 20. Now, let's distribute the -3. -3 × x squared is -3x
1:35 squared. -3 × -5x is a positive 15x. And then we have + 4x squared -12 -8x. All right, let's com- let's group the 10x squared, -3x squared, and positive 4x squared. Let's group the x's, -15x with +15x and -8x and then the last grouping is going to be +20 and -20. Okay. So, let's do that first. Let's just combine the +20 and the -12 here.
2:21 So, we can get rid of those to get +8. Okay. And now let's do the the x's. So, we have -15x and +15x. Those just cancel. So, that's gone. And any other orange? Yes, a -8 x. Okay, that's gone. Now, we just have to do the green ones, the x²'s. We have +10x² and a -3x². That's uh um +7x². And then +4x² gets us + 11x² and that Let's cancel those out quickly. Okay, and that is that is it. That is
3:06 done. Are you up for the challenge? Here's your problem right here. Leave your answer in the comments. Don't forget to like and subscribe. We'll see you in the next video.
From the video’s captions.
