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Multiplying and Distributing Radical Expressions  Problem 4
Alissa Fong
Alissa Fong
MA, Stanford University
Teaching in the San Francisco Bay Area
Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts
Here I have two binomials being multiplied together. So I'm going to use the FOIL process; first, outers, inners, last. When I multiply the first, I have 2 root 10 times regular root 10. That's the same thing as 2 times 10, because root 10 times root 10 is 10.
So 2 times 10 gives me 20, that's my first. Outers, I have 6 from these guys, and then square root of 50. Inners, I have 3 root 50, and then lasts, I have 9 in my outside numbers. And then square root of 5 times square of 5 is regular 5. What I have is 9 times 5 which is 45.
I did a couple steps in my head there, so if I lost you, you might want to go back, and rewatch the start of this video. These firsts and lasts, are regular integers, so they're going to be combined. And then these are like term radicals. So I can combine those.
Let's start with this. 20 take away 45 is 25. Here I have 6 plus 3 which is 3 root 50. A lot of students will box this answer, and think they're done . In fact, I need to simplify further. Square root of 50 could be written as square root of 25 times square root of 2. Square root of 25 is a whole number 5, so really what I'm working with is 3 times regular 5 times root 2. That came with the 25 piece.
Combine all that together, I'll have 25 take away 15 root 2. That might be the answer in the back of your text book. Your textbook might also have factored out a common factor of either positive, or 5. I'm going to show you what it will look like. If I factored out 5, then I would have 5 minus 3 root 2. Your textbook might also have given you this answer. Those are equivalent statements, only this guys has the 5 factored out.
So the first step is the most tricky, the foiling. Make sure you're careful with what's inside the radical, or what's a radical, and what's outside. Then I used a shortcut, knowing that if I was doing 2 times square root of 10, times square root of 10, that was just like 2 times 10 or 20. That's how I went through to find this in this term, then combining like terms, simplifying to get to there.
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Alissa Fong
M.A. in Secondary Mathematics, Stanford University
B.S., Stanford University
Alissa has a quirky sense of humor and a relatable personality that make it easy for students to pay attention and understand the material. She has all the math tips and tricks students are looking for.
Sample Problems (7)
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Multiplying and Distributing Radical Expressions
Problem 1 9,281 viewsMultiply:
(3√6x)(2√6x) 
Multiplying and Distributing Radical Expressions
Problem 2 7,720 viewsSimplify:
√3x(√4x − 5) 
Multiplying and Distributing Radical Expressions
Problem 3 6,612 viewsSimplify:
(4 + √6)(3 − √6) 
Multiplying and Distributing Radical Expressions
Problem 4 5,827 viewsSimplify:
(2√10 + 3√5)(√10 − 3√5) 
Multiplying and Distributing Radical Expressions
Problem 5 1,087 views 
Multiplying and Distributing Radical Expressions
Problem 6 1,307 views 
Multiplying and Distributing Radical Expressions
Problem 7 943 views
Comments (1)
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Katelyn Shahan · 1 year, 4 months ago
I'm sorry, I think I misunderstood the factoring: why wouldn't the answer be 5(5 + 3√2) ? I paused the video to work it out on my own first, and I thought it should be plus 3 instead of minus 3, since we factored out negative 5. What did I do wrong? Thanks in advance!!