Search for tag: "factor"

Simplifying a product involving square roots using the distributive property: Basic

Two examples of distributing radicals into a sum of other radicals and simplifying in the process.

From  Tom Grant 11 plays 0  

Introduction to simplifying a product of radical expressions: Univariate

Just a quick couple of examples, one explaining the relationship between squaring and square rooting and one that just shows how to multiply two radical expressions that need no reduction.

From  Tom Grant 8 plays 0  

Solving rational equations that simplify to quadratic: Binomial denominators & numerators

A The key to solving this kind of equation is multiplying through by the least common denominator to eliminate the fractions first, Then it is a matter of combining like terms on one side of the…

From  Tom Grant 55 plays 0  

Solving a quadratic equation by completing the square: Exact Answers

Two examples are shown here, one relatively easy, then one with some fractions involved.

From  Tom Grant 4 plays 0  

Solving a radical equation that simplifies to a quadratic equation: One radical, advanced

Describes how to approach solving a radical eqaution, then demonstrates the stepss needed. It finishes with a check of the answers, stressing that this is an essential step.

From  Tom Grant 13 plays 0  

Solving an exponential equation by finding common bases: Linear exponents

Shows how to create common bases so that then the exponents can be set equal to each other and that equation can be solved.

From  Tom Grant 22 plays 0  

Adding rational expressions with linear denominators without common factors: Basic

A subtraction of fractionso where the denominators have no factors in common so we simpllly multiply the two together to create the LCD. Then both fractions are adjusted by multiplying each…

From  Tom Grant 9 plays 0  

Complex fraction made of sums involving rational expressions: Multivariate

Simplifies a complex fraction by distributing the LCD of each small fraction across the top and the bottom so that all small fractions can be swept away.

From  Tom Grant 14 plays 0  

Complex fraction made of sums involving rational expressions: Problem type 3

A complex fraction is multiplied through on the top and the bottom by the common denominator of all smaller fractions, eliminating the denominators of those smaller fractions.

From  Tom Grant 11 plays 0  

Adding rational expressions involving different quadratic denominators

Adding ratioinal expressions with quadratic denominators requires factoring each denominator so that the LCD can be determined. Then each fraction is exapanded by multiplying the tops and the…

From  Tom Grant 6 plays 0  

Adding rational expressions with linear denominators with common factors: Basic

This shows how to determine a common denominator when the denominators share at least one factor. A numerical version is included for more understanding, and the rational expressions are added and…

From  Tom Grant 22 plays 0  

Adding rational expressions with multivariate monomial denominators: Basic

This example shows how to factor each denominator and then determine which of these factors are needed to create the least common denominator (LCD). Then the fractions are expanded by multiplying…

From  Tom Grant 6 plays 0  

Adding rational expressions with common denominators & GCF factoring

An example that is easy to combine with subtraction, in this case, because the two fractions have common denominators. However, be aware that there may be a way to simplifying the answer further. …

From  Tom Grant 6 plays 0  

Finding the LCD of rational expressions with quadratic denominators

Each denominator is factored and then any common factor is used only once and all other unique factors complete the LCD

From  Tom Grant 5 plays 0  

Finding the LCD of rational expressions with linear denominators: Common factors.

A demonstration of how factoring is used to discover the minumum number of factors that need to be combined to find the smallest denominator that can be used as the LCD of the two given fractions.

From  Tom Grant 8 plays 0  

Least common multiple of two monomials

A clarification on what common multiple means and why the least common one is larger than or at least as large as either number or expression. Then there follows an example of two multivariate…

From  Tom Grant 7 plays 0