Title: Finding LCM and HCF of Algebraic Expressions – Step-by-Step Lecture Objective: Create an educational video lecture that clearly explains how to find the Lowest Common Multiple (LCM) and Highest Common Factor (HCF) of algebraic expressions using factorization techniques.

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Welcome to our lesson on finding LCM and HCF of algebraic expressions. The Highest Common Factor, or HCF, is the largest expression that divides all given expressions. The Lowest Common Multiple, or LCM, is the smallest expression that is divisible by all given expressions. Just like with numbers, we use factorization to find these for algebraic expressions. Now let's learn how to find the HCF of algebraic expressions. First, factor each expression completely into its prime factors and variables. Next, identify all the common factors between the expressions. Finally, take the lowest power of each common factor. For example, twelve x cubed y squared factors as two squared times three times x cubed times y squared, and eighteen x squared y cubed factors as two times three squared times x squared times y cubed. The common factors are two, three, x, and y. Taking the lowest powers gives us HCF equals six x squared y squared. Now let's find the LCM of algebraic expressions. The process is similar to HCF but with one key difference. First, factor each expression completely. Second, identify all factors that appear in any of the expressions. Third, take the highest power of each factor. Using the same expressions, twelve x cubed y squared and eighteen x squared y cubed, we identify all factors: two, three, x, and y. Taking the highest powers gives us LCM equals two squared times three squared times x cubed times y cubed, which equals thirty-six x cubed y cubed. Let's work through a polynomial example. Find the HCF and LCM of A equals x squared minus four and B equals x squared plus four x plus four. First, we factor each expression. A equals x squared minus four factors as x minus two times x plus two, using difference of squares. B equals x squared plus four x plus four factors as x plus two squared, which is a perfect square trinomial. For the HCF, we take the lowest power of common factors. The only common factor is x plus two to the first power. For the LCM, we take the highest power of all factors: x minus two to the first power and x plus two to the second power. To summarize our lesson on finding LCM and HCF of algebraic expressions: First, factor each expression completely using techniques like common factors, difference of squares, and trinomial factoring. For HCF, take the lowest power of all common factors. For LCM, take the highest power of all factors present. Practice with both simple monomials and more complex polynomials. Remember, mastering factorization techniques is the key to success with these problems.