## Thursday, October 31, 2013

### Special Products - Factoring, 20

Category: Algebra

"Published in Newark, California, USA"

Find the factors for

Solution

Consider the given equation above

In this type of factoring of a polynomial, grouping is needed and we need to group the terms according to their type of variables. In grouping, usually you have to do the trial and error until you get the desired factors. Let's group the first two terms and then another group for the remaining terms as follows

The first group can be factored by the difference of two squares while the other group can be factored by removing of their common factor. Let's factor the grouped terms as follows

The common factor of the above equation is (6x - 5y). Take out their common factor and  therefore, the factors of the given equation are

## Wednesday, October 30, 2013

### Special Products - Factoring, 19

Category: Algebra

"Published in Newark, California, USA"

Find the factors for

Solution:

Consider the given equation above

In this type of factoring of a polynomial, we need to group the terms first according to their type of variables. In grouping, usually you have to do the trial and error until you get the desired factors. In this case for the given equation, let's group the first two terms and then another group for the remaining terms as follows

The common factor at the first group is 2x and y at the second group. Take out their common factor in each group, we have

Since the grouped terms are now the same, we can take out their common factor and therefore, the factors of the given equation are

## Tuesday, October 29, 2013

### Special Products - Factoring, 18

Category: Algebra

"Published in Newark, California, USA"

Find the factors for

Solution:

Consider the given equation above

The two terms are both perfect square but we cannot factor the given equation by the difference of two squares because both terms are positive and the other one must be negative in order to factor the given equation. Let's rewrite the given equation in terms of power as follows

The two terms are now expressed in terms of power or exponent. Since their exponents are multiples of three, then we can factor the given equation by the sum and difference of two cubes. Therefore, the factors are

## Monday, October 28, 2013

### Special Products - Factoring, 17

Category: Algebra

"Published in Newark, California, USA"

Find the factors for

Solution:

Consider the given equation above

Since the two terms have both odd exponents which is 7, then we can factor the given equation by the sum and difference of two like odd powers. Therefore, the factors are

## Sunday, October 27, 2013

### Special Products - Factoring, 16

Category: Algebra

"Published in Newark, California, USA"

Find the factors for

Solution:

Consider the given equation above

Since the two terms have both even exponents, then we can factor the given equation by the sum and difference of two squares as follows

Factor each group by the sum and difference of two cubes as follows

Therefore, the factors are

## Saturday, October 26, 2013

### Special Products - Factoring, 15

Category: Algebra

"Published in Newark, California, USA"

Find the factors for

Solution:

Consider the given equation above

If you will examine the given equation, each terms are perfect cube. (a + b) is considered as a single variable. The given equation can be factored by the sum and difference of two cubes. Therefore, the factors are

## Friday, October 25, 2013

### Special Products - Factoring, 14

Category: Algebra

"Published in Newark, California, USA"

Find the factors for

Solution:

Consider the given equation above

If you will examine the equation above, there's a common factor which is a. Take out their common factor as follows

Since each terms in the parenthesis are perfect cube, then we can factor the grouped terms as the sum and difference of two cubes. Therefore, the factors are