Algebraic Operations - Radicals

Category: Algebra

"Published in Newark, California, USA"

Find the sum of the following:

Solution:

Consider the given equation above

Factor and then rewrite their coefficients into their exponential expression as follows

Take out all the terms that have fourth power and take their fourth root, we have

  
At the third term, there's a denominator which is x² inside the radical sign. We need to rationalize the denominator by multiplying both sides of the fraction by x² in order to eliminate the fraction as follows

Combine similar terms and simplify

Special Products - Factoring, 2

Category: Algebra

"Published in Newark, California, USA"

Find the factors for

Solution:

The given equation above is a quadratic equation where the variables or terms are polynomials like (2x - 1) and (x + 3). 

To test the above equation if it is factorable or not, let's consider the following procedure: if a = 8, b = -2, and c = -3, then using the discriminant formula, we have

Since the value of discriminant is a perfect square, then the given equation is factorable. Consider the given equation above

Factor the above equation in terms of (2x - 1) and (x + 3), we have

Special Products - Rational Functions

Category: Algebra

"Published in Newark, California, USA"

 Write  the product and simplify for

 

Solution:

The given equation above is another good example of special products where a binomial multiplied by another binomial where the terms are rational functions. In this case, we have to do the distribution property of multiplication over addition as follows

The LCD (Least Common Denominator) of the three fractions is (x + y)²(a + b)². Rewrite the three fractions in terms of their LCD and simplify, we have

Since all the terms of the numerator cannot be combined and simplified, then we can leave the final answer as is.