Question
How could you use polynomial identities to factor the expression 
.
Hint:
Here, a and b can be real numbers, variables or multiples of both. We are asked to explain on how to use polynomial identities to factorize the given expression.
The correct answer is: factorize a polynomial fraction
Step 1 of 3:
Factorization of algebraic means to obtain two or more expressions whose product is the given expression. The process of finding two or more expressions whose product is the given expression is called the factorization of algebraic expressions.
Step 2 of 3:
The given expression is x6 - y6 . It can be written as 
. Using the identity, we have:
Step 3 of 3:
Now, apply the identity of cubes to the simplified expression. Thus, we get:
Thus, the factorized form is:
Step 3 of 3:
Now, apply the identity of cubes to the simplified expression. Thus, we get:
Thus, the factorized form is:
We can use multiple identities to simplify or factorize a polynomial fraction
Related Questions to study
How many terms will there be in the expansion of the expression 
. Explain how you know
For the expansion of the expression (x + y)n , we would have n+1 terms.
How many terms will there be in the expansion of the expression . Explain how you know
For the expansion of the expression (x + y)n , we would have n+1 terms.
Factor 
in the form 
. Then find the value of a, b and c.
We use polynomial identities to factorize and expand polynomials to reduce time and space.
Factor in the form . Then find the value of a, b and c.
We use polynomial identities to factorize and expand polynomials to reduce time and space.
The sum of the coefficients in the expansion of the expression (a + b)n is 64. Use Pascal’s triangle to find the value of n.
To find the value of n when the sum of coefficients is given, we have to write them as the power of two. The power would be the value of n.
The sum of the coefficients in the expansion of the expression (a + b)n is 64. Use Pascal’s triangle to find the value of n.
To find the value of n when the sum of coefficients is given, we have to write them as the power of two. The power would be the value of n.
A student says that the expansion of the expression 
has seven terms. Describe and correct the error the student may have made ?
The answer can be found the Pascal’s triangle as well. The expansion of an expression 
has n+ 1 term.
A student says that the expansion of the expression has seven terms. Describe and correct the error the student may have made ?
The answer can be found the Pascal’s triangle as well. The expansion of an expression has n+ 1 term.
Expand the expression (2x - 1)4 .what is the sum of the coefficients?
The answer can be also found using the Pascal’s triangle. For an expression (x + y)n , we would consider the (n+1)th row.
Expand the expression (2x - 1)4 .what is the sum of the coefficients?
The answer can be also found using the Pascal’s triangle. For an expression (x + y)n , we would consider the (n+1)th row.
Use Pascal’s triangle and the binomial theorem to expand (x + 1)4 . Justify your work.
We can use both the binomial theorem and the Pascal’s triangle to get the expansion of any expression.
Use Pascal’s triangle and the binomial theorem to expand (x + 1)4 . Justify your work.
We can use both the binomial theorem and the Pascal’s triangle to get the expansion of any expression.
Emma factored 
Describe and correct the error Emma made in factoring the polynomial.
It is important to recall the law of exponents while to expand polynomial expressions.
Emma factored Describe and correct the error Emma made in factoring the polynomial.
It is important to recall the law of exponents while to expand polynomial expressions.
Expand 
using binomial theorem.
The answer can be found using the Pascal’s triangle. For , we would consider the (n+1)th row as the coefficients.
Expand using binomial theorem.
The answer can be found using the Pascal’s triangle. For , we would consider the (n+1)th row as the coefficients.
Expand using Pascal’s triangle.
The answer can be found using the binomial theorem 
Expand using Pascal’s triangle.
The answer can be found using the binomial theorem
Use binomial theorem to expand expression (x + y)7 .
The answer can be found using the Pascal’s triangle. For an expression (x + y)n , we would have n + 1 term.
Use binomial theorem to expand expression (x + y)7 .
The answer can be found using the Pascal’s triangle. For an expression (x + y)n , we would have n + 1 term.
Use binomial theorem to expand expression (d - 1)4
The answer can be found using the Pascal’s triangle. For an expression , we would have n+ 1 term.
Use binomial theorem to expand expression (d - 1)4
The answer can be found using the Pascal’s triangle. For an expression , we would have n+ 1 term.
Use Pascal triangle to expand the expression (a - b)6 .
The answer can be found using the binomial expansion of
Use Pascal triangle to expand the expression (a - b)6 .
The answer can be found using the binomial expansion of
Use Pascal’s triangle to expand the expression (x + 1)5
The answer can be found using the binomial expansion of
Use Pascal’s triangle to expand the expression (x + 1)5
The answer can be found using the binomial expansion of
How many terms will there be in the expansion of the expression . Explain how you know?
How many terms will there be in the expansion of the expression . Explain how you know?
Find the third term of the binomial expansion 
The expansion of (x + y)n has n+1 terms while expanding. The answer can be found using the Pascal’s triangle or binomial expansion.
Find the third term of the binomial expansion
The expansion of (x + y)n has n+1 terms while expanding. The answer can be found using the Pascal’s triangle or binomial expansion.
