Question
Use Pascal triangle to expand![left parenthesis x plus y right parenthesis to the power of 5](data:image/png;base64,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)
The correct answer is: Using this, the sixth line can be used to find the expansion of . Thus, we have:
ANSWER:
Hint:
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.
We are asked to find the binomial expansion of
using Pascal’s formula.
Step 1 of 1:
The Pascal’s triangle is given by:
![](data:image/png;base64,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)
Using this, the sixth line can be used to find the expansion of
. Thus, we have:
![left parenthesis x plus y right parenthesis to the power of 5 equals x to the power of 5 plus 5 x to the power of 4 y plus 10 x cubed y squared plus 10 x squared y cubed plus 5 x y to the power of 4 plus y to the power of 5.](data:image/png;base64,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)
.Note:
The answer cam also be found by expanding the formula of
.
Related Questions to study
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.
Use polynomial identities to factor the polynomials or simplify the expressions :
![x to the power of 8 minus 9](data:image/png;base64,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)
Use polynomial identities to factor the polynomials or simplify the expressions :
![x to the power of 8 minus 9](data:image/png;base64,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)
How is
obtained from ![left parenthesis x plus y right parenthesis to the power of n minus 1 end exponent](data:image/png;base64,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)
How is
obtained from ![left parenthesis x plus y right parenthesis to the power of n minus 1 end exponent](data:image/png;base64,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)
Use Pascal triangle to expand (x + y)6
The expansion of the polynomial (x + y)6 can be found using the values of 6Cr
Use Pascal triangle to expand (x + y)6
The expansion of the polynomial (x + y)6 can be found using the values of 6Cr
Use polynomial identities to multiply the expressions ?
![open parentheses 25 straight x squared minus 15 straight y squared close parentheses open parentheses 25 straight x squared plus 15 straight y squared close parentheses](data:image/png;base64,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)
Use polynomial identities to multiply the expressions ?
![open parentheses 25 straight x squared minus 15 straight y squared close parentheses open parentheses 25 straight x squared plus 15 straight y squared close parentheses](data:image/png;base64,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)
How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
![12 cubed plus 2 cubed](data:image/png;base64,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)
How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
![12 cubed plus 2 cubed](data:image/png;base64,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)
Use Pascal triangle to expand ![left parenthesis x plus y right parenthesis to the power of 5](data:image/png;base64,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)
The answer cam also be found by expanding the formula of 5Cr .
Use Pascal triangle to expand ![left parenthesis x plus y right parenthesis to the power of 5](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADcAAAASCAYAAAD/ukbDAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAPUJuPDwAAAaBJREFUeNpjYBj64D8WjBVkAXHHIPVEB9R92DxHEOgB8fFBHktHoe4k2XMgjQaD3HPGQHwYi+d+AfEFII7HpskA6rmhAA5DPYkMmKBie4E4Fl1DFxDn0DDDUxPk4SkXhIH4CrrgDiC2xaI4GYdBzVA5anpuLhCHYxEvAOJWJL4lNIawATYgvoUu+AkqgQ2cA2JxJH4iEE+hQczFQ1MQMuCCOlYYzQOfsOjngwYQRr77g8dSDyDug7Jd8IQapZ7zAuJVaGL1QFyLRe0vNPP/QEv6SGwG/yFg8W4gtoeWSMJkVKrEVLLo+UUUiO8CMQcBzxEE+JIlLN3/wlLHULtA+YbE7oPaiy1ffSLFAaCYscYhBxJfA7UsksaeAxXzSlB8F1rEowNLUrMGrqoAZMkmaMbmAeIzRCRLSjy3EIj9gHgptvoKCnKwFDx4AbZKHJTmt6F5xgeIF9PQcwXQEu8SiZU4QXAcKU+B0vU6IJbGom45tASlBQiABoYfCc0vosBgaDj7EXDDUTILNTDIGOAuzzZogYGrXEgbqp1OHSDeQk0DAXAUZOWOXYrsAAAAiHRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtbz4oPC9tbz48bWk+eDwvbWk+PG1vPis8L21vPjxtaT55PC9taT48bXN1cD48bW8+KTwvbW8+PG1uPjU8L21uPjwvbXN1cD48L21hdGg+rS+pUgAAAABJRU5ErkJggg==)
The answer cam also be found by expanding the formula of 5Cr .
Use polynomial identities to multiply the expressions ?
![open parentheses 3 x squared minus 4 x y close parentheses open parentheses 3 x squared plus 4 x y close parentheses](data:image/png;base64,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)
Use polynomial identities to multiply the expressions ?
![open parentheses 3 x squared minus 4 x y close parentheses open parentheses 3 x squared plus 4 x y close parentheses](data:image/png;base64,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)
How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
![27 x to the power of 9 minus 343 y to the power of 6](data:image/png;base64,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)
How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
![27 x to the power of 9 minus 343 y to the power of 6](data:image/png;base64,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)
Use polynomial identities to multiply the expressions ?
![left parenthesis 10 plus 21 right parenthesis squared](data:image/png;base64,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)
Use polynomial identities to multiply the expressions ?
![left parenthesis 10 plus 21 right parenthesis squared](data:image/png;base64,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)
How is ( x + y )n obtained from (x + y)n-1
You could also get the value of from
by just multiplying a ( x + y) with
.
How is ( x + y )n obtained from (x + y)n-1
You could also get the value of from
by just multiplying a ( x + y) with
.
How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
![m to the power of 8 minus 9 n to the power of 10](data:image/png;base64,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)
How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
![m to the power of 8 minus 9 n to the power of 10](data:image/png;base64,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)
Use polynomial identities to multiply the expressions ?
![left parenthesis 7 plus 9 right parenthesis squared](data:image/png;base64,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)
Use polynomial identities to multiply the expressions ?
![left parenthesis 7 plus 9 right parenthesis squared](data:image/png;base64,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)
How can you use polynomial identities to factor polynomials and simplify numerical expressions ? 123 + 23
This can also be done by finding the cube of each values and adding them. But that might be time consuming. Hence, we use these identities.
How can you use polynomial identities to factor polynomials and simplify numerical expressions ? 123 + 23
This can also be done by finding the cube of each values and adding them. But that might be time consuming. Hence, we use these identities.