How to Factor Linear Expressions (Animated)

In algebra, a term is made up of numbers and variables multiplied together.Each term has two main parts: a coefficient, which is the number, and a variable, which is the letter.Like terms are terms that have exactly the same variables with the same exponents.For example, three x and five x are like terms because they both have just x.But two y is different because it has y instead of x.Let's look at a more complex example with multiple terms.We can identify like terms by looking for terms with the same variables.When we combine like terms, we add their coefficients but keep the same variable.Two x plus four x equals six x, and three y plus y equals four y.Let's try one more example with more complex terms.Terms with x squared are like terms, and terms with x y are like terms.Combining like terms gives us eight x squared plus six x y.To find the Greatest Common Factor, we start with simple numbers.For twelve, we list out all its factors: one, two, three, four, six, and twelve.For eighteen, the factors are: one, two, three, six, nine, and eighteen.The common factors between twelve and eighteen are one, two, three, and six.Six is the greatest number that appears in both lists, making it our Greatest Common Factor.Now let's extend this concept to algebraic terms.For six x squared, we need to consider both the numerical factors and the variables.Nine x has its own set of numerical factors, and only one x.Let's tackle a more complex example with multiple variables.For twelve x cubed y, we break down both the numerical and variable parts.Similarly for eighteen x squared y squared, we identify all factors.For variables, we take the minimum power of each variable that appears in all terms.Therefore, the Greatest Common Factor is six x squared y.To factor out the GCF, we'll start with the expression 15x squared y plus 25xy squared.We've identified that the GCF is 5xy.To factor, we divide each term by the GCF. For the first term, fifteen x squared y divided by five xy gives us three x. For the second term, twenty-five xy squared divided by five xy gives us five y.Now we can write our factored expression as five xy times the quantity three x plus five y.Let's verify our answer by distributing the GCF back to each term.First, distribute five xy to three x and five y separately.This gives us fifteen x squared y plus twenty-five xy squared, which matches our original expression.Now, let's look at some common mistakes to avoid when factoring out the GCF.A common error is forgetting to include all variables in the GCF. Here, someone only factored out the number 5, which is incorrect.Another mistake is not dividing all terms completely by the GCF, leaving extra variables that should have been removed.Here's a practice example for you to try: Factor twelve x cubed y squared plus eighteen x squared y cubed.