Question
How are Pascal’s triangle and binomial expansion such as (a + b)5 related?
Hint:
Pascal's Triangle gives us the coefficients for an expanded binomial of the form (a + b)n , where n is the row of the triangle. The Binomial Theorem tells us we can use these coefficients to find the entire expanded binomial, with a couple extra tricks thrown in.
The correct answer is: (x + y)n
Step 1 of 1:
![](data:image/png;base64,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)
Pascal's Triangle is a method to know the binomial coefficients of terms of binomial expression (x + y)n , where n can be any positive integer and x, y are real numbers. Pascal Triangle is represented in a triangular form, it is kind of a number pattern in the form of a triangular arrangement.
The binomial expansion of (a + b)5 is:
![table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell left parenthesis a plus b right parenthesis to the power of 5 equals 5 C subscript 0 a to the power of 5 plus 5 C subscript 1 left parenthesis a right parenthesis to the power of 4 left parenthesis b right parenthesis plus 5 C subscript 2 left parenthesis a right parenthesis cubed left parenthesis b right parenthesis squared plus 5 C subscript 3 left parenthesis a right parenthesis squared left parenthesis b right parenthesis cubed plus 5 C subscript 4 left parenthesis a right parenthesis left parenthesis b right parenthesis to the power of 4 plus 5 C subscript 5 left parenthesis b right parenthesis to the power of 5 end cell row cell equals a to the power of 5 plus 5 a to the power of 4 b plus 10 a cubed b squared plus 10 a squared b cubed plus 5 a b to the power of 4 plus b to the power of 5 end cell end table](data:image/png;base64,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)
Here, the coefficients of the expansions are the elements of the sixth row of the Pascal’s triangle.
Here, the coefficients of the expansions are the elements of the sixth row of the Pascal’s triangle.
You can find the expansion of (x + y)n using both Pascal’s triangle and binomial expansion.
Related Questions to study
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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)
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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)
Use polynomial identities to factor the polynomials or simplify the expressions :
![216 plus 27 y to the power of 12](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFwAAAATCAYAAAAd4WrhAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAitJREFUeNrtV8FHREEcfp6VrESyVjrEWmulw16SJIl02EO6rKwkiZU97T+QTl06dE86JIkkydp7VhIrWR2ydOzQNVlrxes3fIfnmbdvZt7M6/I+PvbNjLfffPOb3+/3LCuGKnLEfeIrZ84B+8RHYja2KzwuiBUY6webWCW+xHbpgyOwphfbFJ3hS8QH7+AC8Yb4jbzD8tKmYv5yY5Z4jfeyU76HAJ0Q1e4E0IThE8jhGe8EO4EycQTP01hYDpG/KjA4h+dRGNHUbLisdi9KxFMDhrN912G6EKaIbcU/Y5tuRZAbw2hnSCMAhjXrZCY3EGRS6CmaciIRYSYMFy1U7AYWPGNnxA3O2hrxUFAnMzsvK3geV1PFlHeZq2TAcBHte6hDXmwTjzxjSWKHOB5QE0TmuGBX7BkFScWUHnLYLbGLYtYKKMS6DBfRPoU1Cc5cEYXejQOfw9GCMeIdcTWEKQ6a/SI2ZcOADj4ELIUuwtGonRXaZZ85FsVvrucU8SNknvdFBoKzIaOQtWiTnHGWLz8NRbio9hJy7CB0Xb+Pkb+1I4/2KKnh2jcQ1Tz0DRguqt1GfSkErGviADOIblu32WnkrYSmwlb1qfR55E6dhstoX+d99XFwTlwjXhK3TER3XaWNGWDKEDa26zJiDr3ximbDZbRfEXcE1tXQHrYtQ5AtVCLrUrjmP8RfHMDiP2v/QmEVuQkOojxGBGBGP8U2RIcGPp5iRIAZ1AUj+ANBkK+WPOsIzgAAAIJ0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW4+MjE2PC9tbj48bW8+KzwvbW8+PG1uPjI3PC9tbj48bXN1cD48bWk+eTwvbWk+PG1uPjEyPC9tbj48L21zdXA+PC9tYXRoPl4oa1YAAAAASUVORK5CYII=)
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
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Use binomial theorem to expand
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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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)
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,iVBORw0KGgoAAAANSUhEUgAAADcAAAASCAYAAAD/ukbDAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAPUJuPDwAAAcpJREFUeNpjYBgewByIDwLxDyD+D8UYIAuIOwapBzqg7kMHWkB8Doh18GnWA+LjgzyGjkLdiQwWArEtMRoNBrnnjIH4MJrYayCOBuKHQHwLiEPRNRlAPTcUwGGoJ2HgDxDPBmI+IGaDshORNXQBcQ6NHPOfyubloZULoNhiQuLzQGMRDnbgSLfJOAqYZqgcNT03F4jDsYgXAHErEt8SiPci8UExJYjEB8XeGWQDPkEFsQFQSSSOxAdF+RQaxFw8NAUhAy5ozAijOf4TWkG4EJosWaBu82BAS7e4AEhhH5TtghZq1PScFxCvQhOrB+JaLGp/ofFBBcpdIH6JrUD5Q8Di3UBsD8QX0EIRl2cIYWwAZO4VJL4o1MEcRHgOL8CXLGHp/heWOobaBco3JHYf1F50gJ4sCQJQzFjjkAOJr4FaFkljz4GKeSUovotWCuIqUAgCXFUByJJN0IzNAy2FhGnoOVDB4AfES4E4FoeaHCwFD16ArRIHpfltaJ7xAeLFNPRcAbRKuERCJU4UOI6Up0Dpeh0QS2NRtxy9qKUiCIAGhh8JzS+iwGBoOPsRcMNRMgs1MMgY4C7PNmiBgatcSBuqHU5Qf2wLNQ0EAJ7kZvB0fLxLAAAAiHRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtbz4oPC9tbz48bWk+eDwvbWk+PG1vPis8L21vPjxtaT55PC9taT48bXN1cD48bW8+KTwvbW8+PG1uPjY8L21uPjwvbXN1cD48L21hdGg+AobkmAAAAABJRU5ErkJggg==)
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.