Question
Use binomial theorem to expand .![open parentheses s squared plus 3 close parentheses to the power of 5](data:image/png;base64,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)
The correct answer is: For the expansion of an expression , we would have n+1 terms. This is something you need to keep in mind.
ANSWER:
Hint:
The binomial expansion is
, here
.
We are asked to use binomial theorem to expand
.
Step 1 of 2:
The given expression is ,
. The value of n=5, hence there are 5+1=6 terms in the expressions.
Step 2 of 2:
Substitute the values of
in the binomial equation to get the expansion:
![open parentheses s squared plus 3 close parentheses to the power of 5 equals 5 C subscript 0 open parentheses s squared close parentheses to the power of 5 plus 5 C subscript 1 open parentheses s squared close parentheses to the power of 4 left parenthesis 3 right parenthesis plus 5 C subscript 2 open parentheses s squared close parentheses cubed left parenthesis 3 right parenthesis squared plus 5 C subscript 3 open parentheses s squared close parentheses squared left parenthesis 3 right parenthesis cubed plus 5 C subscript 4 open parentheses s squared close parentheses left parenthesis 3 right parenthesis to the power of 4 plus 5 C subscript 5 left parenthesis 3 right parenthesis to the power of 5](data:image/png;base64,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)
![equals s to the power of 10 plus 5 open parentheses s to the power of 8 close parentheses left parenthesis 3 right parenthesis plus 10 open parentheses s to the power of 6 close parentheses left parenthesis 9 right parenthesis plus 10 open parentheses s to the power of 4 close parentheses left parenthesis 27 right parenthesis plus 5 open parentheses s squared close parentheses left parenthesis 81 right parenthesis plus left parenthesis 243 right parenthesis](data:image/png;base64,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)
![equals s to the power of 10 plus 15 s to the power of 8 plus 90 s to the power of 6 plus 270 s to the power of 4 plus 405 s squared plus 243](data:image/png;base64,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)
Thus, the expansion is:![open parentheses s squared plus 3 close parentheses to the power of 5 equals s to the power of 10 plus 15 s to the power of 8 plus 90 s to the power of 6 plus 270 s to the power of 4 plus 405 s squared plus 243](data:image/png;base64,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)
Note:
For the expansion of an expression
, we would have n+1 terms. This is something you need to keep in mind.
Related Questions to study
Use polynomial identities to factor the polynomials or simplify the expressions :
![216 plus 27 y to the power of 12](data:image/png;base64,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)
Use polynomial identities to factor the polynomials or simplify the expressions :
![216 plus 27 y to the power of 12](data:image/png;base64,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)
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 :
![4 x squared minus y to the power of 6](data:image/png;base64,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)
Use polynomial identities to factor the polynomials or simplify the expressions :
![4 x squared minus y to the power of 6](data:image/png;base64,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)
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 :
![x cubed minus 27 y cubed](data:image/png;base64,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)
Use polynomial identities to factor the polynomials or simplify the expressions :
![x cubed minus 27 y cubed](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEkAAAATCAYAAADcZiBNAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAclJREFUeNpjYCAd/IfiX0B8AYjdGIYHoJm/NID4IcPwA1T1FxMQvxuGgUQ1fwkD8RQgThxmAUQ1f8HybyyNHGoNxGuA+BNSGRGNxx248ID7iw+IW4E4jQaBdBCII4GYB8rXAuKjUDFiQCgQzx5M/vpBp2wgD8SXiFAnDsSHgZiDFv5KBuIOLOLNUDlswBaIz9CxvCAmQjYBsQGa2FwgDseitgCaakjy1zloTMBAIrQQw5ZvQQ7eAY1hegBLaJbDBzKAuBaLeDwQd6GJcQHxLWhBTZK/PIC4D8p2AeK9g6TGAWWdk9ACHV92BKlhwSLnBcSr0MTqcQQoUWA3ENtDaxRhKtWClNRAgkC8gYgWMKiwd8RTrV9B4osC8V1Kyq0CaLWrNwhSkBI0gFSIqM22EVDzDYndB/UnRe2TPhKqW1p2DWZDyw5CreMbWAprdHAYGuhK0FTERG6sbYI6igdaugsPUACJQ8sQFiLUBkCzGiGwEIj9gHgpuY1FUWhyRQ4UHyBePECBtAWakogBy4nsQhRAmwKXyHEQGxCvA2JpHA7wGMBhC2IK+pfQwp2YFPcfmppGAQ4ACpzjo8GAH2yDNkhHAQ6gAy3nyAIATxJ1oljiS+EAAACddEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1zdXA+PG1pPng8L21pPjxtbj4zPC9tbj48L21zdXA+PG1vPiYjeDIyMTI7PC9tbz48bW4+Mjc8L21uPjxtc3VwPjxtaT55PC9taT48bW4+MzwvbW4+PC9tc3VwPjwvbWF0aD5Gqg6sAAAAAElFTkSuQmCC)
Use Pascal triangle to expand![left parenthesis x plus y right parenthesis to the power of 6](data:image/png;base64,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)
Use Pascal triangle to expand![left parenthesis x plus y right parenthesis to the power of 6](data:image/png;base64,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)
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.