Question
Use polynomial identities to factor the polynomials or simplify the expressions :
The correct answer is: Hence, the factor form is 216 + 27y^12 = (6 + 3y^4) (36 - 18y^4 + 9y^8)
ANSWER:
Hint:
, where a and b can be real values, variables or multiples of both.
We are asked to use polynomial identities to factorize or simplify the expression.
Step 1 of 2:
The given expression is .
.
Step 2 of 2:
Use the polynomial identity to simplify the expression;
Hence, the factor form is 
Note:
The multiplication of algebraic expressions is a method of multiplying two given expressions consisting of variables and constants.
Related Questions to study
Explain why the middle term 
is 10x.
In the Binomial Expansion's middle term, in the expansion of (a + b)n, there are (n + 1) terms. Therefore, we can write the middle term or terms of (a + b)n based on the value of n. It follows that there will only be one middle term if n is even and two middle terms if n is odd.
The binomial expansions of (x + y)n are used to find specific terms, such as the term independent of x or y.
Practice Questions
1. Find the expansion of (9x - 2y)12's coefficient of x5y7.
2. In the expansion of (2x - y)11, locate the 8th term.
Explain why the middle term is 10x.
In the Binomial Expansion's middle term, in the expansion of (a + b)n, there are (n + 1) terms. Therefore, we can write the middle term or terms of (a + b)n based on the value of n. It follows that there will only be one middle term if n is even and two middle terms if n is odd.
The binomial expansions of (x + y)n are used to find specific terms, such as the term independent of x or y.
Practice Questions
1. Find the expansion of (9x - 2y)12's coefficient of x5y7.
2. In the expansion of (2x - y)11, locate the 8th term.
Use binomial theorem to expand 
.
Use binomial theorem to expand .
Use polynomial identities to factor the polynomials or simplify the expressions :
Use polynomial identities to factor the polynomials or simplify the expressions :
How can you use polynomial identities to rewrite expressions efficiently ?
Polynomial identities are equations that are true for all possible values of the variable and numbers.
How can you use polynomial identities to rewrite expressions efficiently ?
Polynomial identities are equations that are true for all possible values of the variable and numbers.
Use binomial theorem to expand (2c + d)6
The expansion of the expression can also be found using the Pascal’s triangle. But, it is necessary to remember the values of the triangle to write down the expansion.
Use binomial theorem to expand (2c + d)6
The expansion of the expression can also be found using the Pascal’s triangle. But, it is necessary to remember the values of the triangle to write down the expansion.
Use binomial theorem to expand 
.
Use binomial theorem to expand .
Use binomial theorem to expand (x - 1)7
For the expansion of an expression (x + y)n , we would have n+1 terms. This is something you need to keep in mind.
Use binomial theorem to expand (x - 1)7
For the expansion of an expression (x + y)n , we would have n+1 terms. This is something you need to keep in mind.
Use polynomial identities to factor the polynomials or simplify the expressions :
Use polynomial identities to factor the polynomials or simplify the expressions :
Use Pascal triangle to expand
Use Pascal triangle to expand
Use binomial theorem to expand (s2 + 3)5
For the expansion of an expression (x + y)n , we would have n+1 terms. This is something you need to keep in mind.
Use binomial theorem to expand (s2 + 3)5
For the expansion of an expression (x + y)n , we would have n+1 terms. This is something you need to keep in mind.
Use polynomial identities to factor the polynomials or simplify the expressions :
Use polynomial identities to factor the polynomials or simplify the expressions :
Use Pascal triangle to expand
Use Pascal triangle to expand
Use polynomial identities to factor the polynomials or simplify the expressions :
Use polynomial identities to factor the polynomials or simplify the expressions :
Use Pascal triangle to expand
Use Pascal triangle to expand
Use binomial theorem to expand (x - 3)4
For the expansion of an expression (x + y)n , we would have n+1 terms. This is something you need to keep in mind.
Use binomial theorem to expand (x - 3)4
For the expansion of an expression (x + y)n , we would have n+1 terms. This is something you need to keep in mind.
