Think about what the words sum, two, and cube mean when combined in this way.
See solution.
Practice makes perfect
To decide if an equation fits in the sum of two cubes pattern, there are three conditions that must be satisfied.
There are exactly two terms.
The operation between both terms is addition.
Both terms are perfect cubes.
Let's see some examples.
Example 1
Decide whether the expression fits the sum of two cubes pattern.
8x^6+27We can see that there are two terms and the operation between them is addition. Therefore, the first two conditions are satisfied. Finally, let's see if the terms are perfect cubes.
Both terms are now written as perfect cubes. The third condition is also satisfied. Therefore, the given expression fits the sum of two cubes pattern.
Example 2
Decide whether the expression fits the sum of two cubes pattern.
x^6+27x^3+8
The above expression cannot be simplified to only two terms. This means that it fails the first condition. Therefore, it does not fit the sum of two cubes pattern.
Example 3
Decide whether the expression fits the sum of two cubes pattern.
x^3-8
The above expression contains two terms that are perfect cubes.
x^3-2^3
However, instead of addition it has subtraction. This means it fails the second condition and it does not fit the sum of two cubes pattern.
Example 4
Decide whether the expression fits the sum of two cubes pattern.
x^3+9
The above expression consists of the sum of two terms. Although the first term is a perfect cube, the second one is not.
x^3+3^2
Therefore, it fails the third condition and does not fit the sum of two cubes pattern.
