How do you distribute a negative sign across an expression?

You distribute a negative sign by multiplying it with each term in the expression, effectively changing the sign of each term.

What is the simplified form of '16x + 14 - (3x^2 + x - 9)'?

The simplified form is '-3x^2 + 15x + 23'.

How do you combine like terms in an algebraic expression?

Combine like terms by adding or subtracting the coefficients of terms that have the same variable part.

What does it mean to subtract an entire expression?

Subtracting an entire expression means adding the negative of that expression, or distributing a negative sign across all its terms.

What's the importance of maintaining the negative sign with terms it belongs to?

Maintaining the negative sign is crucial as it affects the result by changing the value and the sign of the term when combined with others.

Example 3: Subtracting polynomials | Algebra I | Khan Academy

00:02:07

https://www.youtube.com/watch?v=5ZdxnFspyP8

Summary

TLDRThe video explains how to simplify the expression 16x + 14 minus the entire expression 3x^2 + x - 9. The process involves adding the opposite of the second expression by distributing the negative sign to each term. This distribution changes the signs resulting in -3x^2, -x, and +9. By combining like terms, the x squared term remains -3x^2, the linear terms combine to 15x, and the constants add up to 23, forming the simplified result: -3x^2 + 15x + 23.

Takeaways

🤔 Distribute the negative: Apply the negative sign across the entire expression 3x^2 + x - 9.
💡 Combine like terms: Identify and simplify terms of the same degree.
➡️ Highest degree term: Recognize the importance of ordering terms by degree.
🧮 Simplification result: Final simplified form is -3x^2 + 15x + 23.
🔄 Negative sign effects: Changes each term's sign in the expression.
📊 Linear term analysis: 16x - x simplifies to 15x.
📝 Constant term sum: 14 + 9 results in 23.
🧠 Problem-solving steps: Detailed procedural breakdown for clarity.

Timeline

00:00:00 - 00:02:07
The instructor explains that to simplify the expression "16x plus 14 minus (3x squared plus x minus 9)," one should subtract the entire expression, which equals adding the opposite of that expression. This involves distributing a negative sign across the terms in the parentheses. First, rewrite the expression as "16x + 14 + (-1) * (3x^2 + x - 9)." Distribute the negative sign: "16x + 14 - 3x^2 - x + 9." Simplify by combining like terms: the highest degree term "-3x^2," next the x terms "16x - x = 15x," and constant terms "14 + 9 = 23." Thus, the final simplified expression is "-3x^2 + 15x + 23."

Mind Map

Video Q&A

How do you distribute a negative sign across an expression?
You distribute a negative sign by multiplying it with each term in the expression, effectively changing the sign of each term.
What is the simplified form of '16x + 14 - (3x^2 + x - 9)'?
The simplified form is '-3x^2 + 15x + 23'.
How do you combine like terms in an algebraic expression?
Combine like terms by adding or subtracting the coefficients of terms that have the same variable part.
What does it mean to subtract an entire expression?
Subtracting an entire expression means adding the negative of that expression, or distributing a negative sign across all its terms.
What's the importance of maintaining the negative sign with terms it belongs to?
Maintaining the negative sign is crucial as it affects the result by changing the value and the sign of the term when combined with others.

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00:00:00
Simplify 16x plus 14 minus the entire expression 3x
00:00:05
squared plus x minus 9.
00:00:08
So when you subtract an entire expression,
00:00:10
this is the exact same thing as having 16x plus 14.
00:00:16
And then you're adding the opposite of this whole thing.
00:00:19
Or you're adding negative 1 times 3x
00:00:24
squared plus x minus 9.
00:00:27
Or another way to think about it is you
00:00:29
can distribute this negative sign along all of those terms.
00:00:32
That's essentially what we're about to do here.
00:00:34
We're just adding the negative of this entire thing.
00:00:37
We're adding the opposite of it.
00:00:39
So this first part-- I'm not going to change it.
00:00:41
That's still just 16x plus 14.
00:00:43
But now I'm going to distribute the negative sign here.
00:00:46
So negative 1 times 3x squared is negative 3x squared.
00:00:52
Negative 1 times positive x is negative
00:00:56
x because that's positive 1x.
00:00:59
Negative 1 times negative 9-- remember,
00:01:02
you have to consider this negative right over there.
00:01:04
That is part of the term.
00:01:05
Negative 1 times negative 9 is positive 9.
00:01:08
Negative times a negative is a positive.
00:01:11
So then we have positive 9.
00:01:14
And now we just have to combine like terms.
00:01:16
So what's our highest degree term here?
00:01:17
I like to write it in that order.
00:01:19
We have only one x squared term, second-degree term.
00:01:22
We only have one of those.
00:01:23
So let me write it over here-- negative 3x squared.
00:01:26
And then what do we have in terms of first-degree terms,
00:01:29
of just an x, x to the first power?
00:01:30
Well, we have a 16x.
00:01:33
And then from that, we're going to subtract an x, subtract 1x.
00:01:36
So 16x minus 1x is 15x.
00:01:40
If you have 16 of something and you subtract 1 of them away,
00:01:43
you're going to have 15 of that something.
00:01:45
And then finally, you have 14.
00:01:48
You could view that as 14 times x to the 0 or just 14.
00:01:51
14 plus 9-- they're both constant terms,
00:01:55
or they're both being multiplied by x to the 0.
00:01:57
14 plus 9 is 23.
00:02:01
And we're done.
00:02:01
Negative 3x squared plus 15x plus 23.