Factorization with substitution | Polynomial factorization | Algebra 2 | Khan Academy

TL;DR

Learn how to factor expressions by identifying U and V, which are either constant integers or single variable expressions, and using the pattern U plus V squared.

Transcript

• [Instructor] We're told that we want to factor the following expression that they have right here and they say that we can factor the expression as U plus V squared where U and V are either constant integers or single variable expressions. What are U and V? And then they ask us to actually factor the expression. So pause this video and see if you... Read More

Key Insights

• ➕ U plus V squared is a pattern used to factor expressions.
• 😍 U and V can be constants, integers, or single variable expressions.
• 🇻🇮 Factoring expressions using U plus V squared involves determining the values of U and V that satisfy the pattern.
• ❎ The pattern U plus V squared = U squared + 2UV + V squared is derived from the square of a binomial.
• 🇻🇮 The middle term in the expression must match 2UV for it to be factored using U plus V squared.
• 🇻🇮 Factoring an expression using U plus V squared simplifies the expression by expanding it into U plus V times U minus V.

Questions & Answers

Q: What is the pattern for factoring an expression using U plus V squared?

The pattern is U plus V squared = U squared + 2UV + V squared.

Q: How do you determine the values of U and V in an expression?

To determine U and V, equate U squared to the first term and V squared to the second term in the expression.

Q: Can you clarify how U plus V squared can be expressed in terms of U and V?

U plus V squared = U squared + 2UV + V squared. This expression represents the square of a binomial.

Q: How can you verify that an expression can be factored using U plus V squared?

By checking if the middle term of the expression can be written as 2UV, following the pattern U plus V squared = U squared + 2UV + V squared.

Summary & Key Takeaways

• The video explains how to factor expressions using the pattern U plus V squared.

• U plus V squared is equal to U squared plus 2UV plus V squared.

• U and V can be determined by equating U squared to the first term and V squared to the second term in the expression.