Search for tag: "factors"

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 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 rational equation that simplifies to quadratic: Binomial denominators, constant numerators

The key to solving this equation is eliminating the fractions first by multiplying by the least common denominator and dividingout equal factors. Note that the integer term must be multiplied by…

From  Tom Grant 17 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  

Rational exponents: Product rule

A simple demonstration of how the product rule forexponents still applies when the exponents are fractions

From  Tom Grant 12 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  

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  

Dividing rational expressions involving linear expressions

A brief informal reasoning of why any division can be changed to a multiplication by reciprocating the second number or fraction, i. e. the number going into the other number. Then an example of…

From  Tom Grant 6 plays 0  

Multiplying rational expressions made up of linear expressions

This is a quick example of factoring the numerator and denominator of a combined fraction where all the factors are separated in order to find those that divide to one.

From  Tom Grant 5 plays 0