Combining like terms with distributionYouTube↗  IA↗(long shot)
Education  170.8K views 135 likes 13 dislikes   01 Dec 2015
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لدي تعبير جبري هنا.
- [Voiceover] So I have an expression here.
ثلاثة ضرب كل التعبير (خمسة س زائد ستة)،
Three times the entire expression 5x plus six,
ثم زائد التعبير (سبعة س زائد اثنين)
and then plus the expression 7x plus two
وكل التعبير ضرب أربعة.
and all of that times four.
أوقفوا الفيديو قليلا،
And what I encourage you to do is pause this video
كي ترون إن كان بإمكانكم تبسيط هذا التعبير.
and see if you can simplify this expression.
سأعطيكم تلميحا هنا.
And I'll give you a hint.
ستقوم بالتوزيع،
You're gonna have to do some distribution
ثم دمج الحدود المتشابهة.
and then some combining of like terms.
أفترضُ الآن أنكم جرّبتم الحل.
All right, now I'm assuming you've had a go at it.
لنحلّها سويًا الآن.
Now let's work through this together.
كما أشرت، عندما أرى ثلاثة ضرب
So as I mentioned, when I see this three times
كل التعبير الجبري (خمسة س زائد ستة)،
the entire expression 5x plus six,
أريد توزيع هذه الثلاثة.
I want to distribute that three.
سأضرب الثلاثة في خمسة س
So I want to multiply that three times 5x
ثم أضربها في الستة.
and that three times the six.
ثلاثة ضرب خمسة س، لو كان لدي خمسة س
So three times 5x, well if I have five Xs
وثلاثة ضرب خمسة س، يصبح لدي خمسة عشر س.
and I have three times that, I'm gonna have 15 Xs.
ثم ثلاثة ضرب ستة يساوي ثمانية عشر.
And then three times six is 18.
بسّطنا هذا الجزء من التعبير الجبري
So this part of the expression we have now simplified
إلى خمسة عشر س زائد ثمانية عشر.
to 15x plus 18.
لنحل الجزء المتبقي.
Now let's do the next part.
لدي هنا التعبير الأكبر مكتوبًا قبل
So here I have this larger expression written before
الأربعة، لكن أريد الحل بنفس الطريقة.
this four but I wanna do the same thing.
أوزع العدد أربعة.
I just wanna distribute the four.
لا يهم إذا كنت أضاعف،
It doesn't matter whether I'm multiplying,
إن كان العدد موجود على الجهة اليسرى
if I have the three or if I have the number on the left side
أو اليمنى، لذا نوزع هذه الأربعة.
or the right side, so let's distribute this four.
أضرب أربعة في سبعة س وأربعة ضرب اثنين.
I wanna do four times 7x and I wanna do four times two.
أربعة ضرب سبعة س، الناتج ثمانية وعشرون س.
Four times 7x, well that's going to be 28x,
ثمانية وعشرون س.
28x.
ثم أربعة ضرب اثنين يكون الناتج ثمانية.
And then four times two is going to be eight.
أوشكنا على الانتهاء.
So we're almost there.
هذا الجزء من التعبير الجبري بسّطناه إلى ثمانية وعشرين زائد س ثمانية
This part of our expression has simplified to 28x plus eight
والآن يمكننا جمع الحدود المتشابهة.
and now we can combine similar terms.
لدينا خمسة عشر س،
So we have 15 Xs,
نضيفها إلى ثمانية وعشرين س،
and then we can add that to 28 Xs.
أريد الكتابة هنا بلون مختلف.
Let me do this in a different color.
إن كان لدي خمسة عشر من شيء ما وأضيف عليه ثمانية عشر
If I have 15 of something and I add 28 of something
من الشيء نفسه،
of that same something to it,
ماذا سيكون لدي. ثلاثة وأربعون س.
well then I'm gonna have what, 43 Xs.
ثلاثة وأربعون س.
So 43 Xs.
خمسة عشر س زائد ثمانية وعشرين س، أضفت المعاملين هنا،
15x plus 28 Xs, I added the coefficients there,
الناتج ثلاثة وأربعون س.
that's gonna be 43 Xs.
ثم ثمانية عشر زائد ثمانية.
And then 18 plus eight.
سأغير اللون مجددًا.
Hey, let me do this in a new color.
ثمانية عشر زائد ثمانية يساوي ستة وعشرين.
So 18 plus eight is going to be 26.
انتهينا.
And we're done.
بسّطنا هذا التعبير الجبري الأطول.
We've simplified this longer expression.
وزّعنا ثم جمعنا
We did some distribution then we combined
الحدود المتشابهة للحصول على ثلاثة وأربعين سين زائد ستة وعشرين.
some terms to get 43x plus 26.
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