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### Course: College Algebra>Unit 10

Lesson 5: Factoring using structure

# Factorization with substitution

Unravel the mystery of algebraic expressions with factorization using substitution! This lesson explores how to simplify complex expressions by identifying patterns and substituting variables. By using U+V² and U+V x U-V structures, you can easily transform and factor expressions!

## Want to join the conversation?

• Are the variables U and V always used for quadratic patterns?
• U and V are just shortening the function. If you do programming, you use functions so you don't have to always type the long code over and over again; you will call the function. In here, they are just shortening each of the parenthesis into one letter.

Hope that helps!
• why isnt V equals to + or - 3y^3, Sal just put it as 3y^3
• Well, you are right. It CAN be 3y^3 or -3y^3. But it doesn't matter because when you are substituting either one into the equation (U+V)(U-V), the results are the same.
When Substituting 3y^3:
(U+3y^3)(U-3y^3)
When Substituting -3y^3:
(U+-3y^3)(U--3y^3) = (U-3y^3)(U+3y^3)
It's basically the same thing but switched the orders of (U+V) and (U-V). So the answer is that you are right, it's a good question though. It just doesn't matter.
• what exactly does it mean to "factor" something?
• It means to break something up into the product of two things. For example, if I wanted to factor 4, I could write it as 2 * 2. The same way, if you want to factor x^2 + 4x + 4, you could write it as (x+2)(x+2). Does this help?
• Im now ahead of my math class a bit, so let me see if i understand this right.
- It's asking us to make a pattern
- (U+v)^2 is acting kinda like X?
-U falls into place for the first part of the problem and V for the last meaning 2u and 2v is the third part and we're seeing if it matches up?
• I think using U and V, especially handwritten, can make it difficult to follow since they are so similar. Is this the standard variables for this sort of question or just a khan academy thing?
• Well variables are just symbols that represent a value that is still unknown. U and V can be any other letters. Whether or not it's standard, like "y=mx+b", I'm not sure.
(1 vote)
• Why is y3 the square root of y6? 3•3 is 9, not 6.
• Because (y³)²=y⁶.
(y³)²=(y·y·y)²=(y·y·y)(y·y·y)=y⁶.

When two exponential expressions with the same base are multiplied, the exponents are added, not multiplied, and so taking the square root of the expression halves the exponent instead of taking its square root.
• What do is really mean to factor something?
(1 vote)
• To factor an expression means to break the expression into the product of numbers/functions that when multiplied together will equal the original expression.
• I was stuck on this for weeks now