Question
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==)
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 5 (x + y)5 using Pascal’s formula.
The correct answer is: 5Cr
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 5 (x + y)5 . Thus, we have:
.
The answer cam also be found by expanding the formula of 5Cr .
Related Questions to study
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,iVBORw0KGgoAAAANSUhEUgAAAE4AAAARCAYAAABzcpo/AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAhJJREFUeNrtmDFIAlEcxkUkQlokIkREkIhoaIkQiZAgJEIaAglnwdEpiIZoiJaGBteGiIZAQiKiLUQaIpBoaIggmiJCcIgIEcG+B9/Fcbwz9d55GX3wA+//7u793/fe+79Dl0uNwqAAPkEdXIE5V39oHGyCO5P2BHggCdWd34MUcBPxu9Inxh2BDGhK2qKgBIZJkTFlqnDmNAVpZj9JZtwpiOmuxS46U9mpWMLPYBZM8uXhP2DcO3eQJjdjyjQCrsEhyIMcGLJhcDHWzxrr6YnCCWq2GaurHJA4GOK66wkaqFJxbv8ZzrwHpFm0R3u04jyqV1xDEqspNq5ssrqSYLdHNU78PjfetAXWOXtiq72BV7DEdh/YA1W6vqF7VhzlEd31IreU3ZOj1Z1byVjWOJYDbmuRd7ZD46I8SX0sRyWdH9/Ks8MyPyfEsgyx6Pv50CrjQa4obYuI+y4Yq/FdfsXGPYFpSTxEY4xjydK0GM0NMDevxDAjxoPvsZXxovGS7ur1AvZN4qrNaaUkJzGm+15McLXVJWPJSN5R5feYMrk5a94O493Wkp9odaoWDSt7zJCLyO1D8qzHQs6mijAhq3EnNAhu2sgtakfOKdYDq3EnNA+2nco5Z1ITOo07oR0Wfn1uaZOc06o7L8iO2S7idkocXCtggNcB/qux7GTOVdYKq3E7tcAa1eB35DGY+uU5/8uoL6Pkk/6fgj56AAAAnXRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtc3VwPjxtaT5tPC9taT48bW4+ODwvbW4+PC9tc3VwPjxtbz4mI3gyMjEyOzwvbW8+PG1uPjk8L21uPjxtc3VwPjxtaT5uPC9taT48bW4+MTA8L21uPjwvbXN1cD48L21hdGg+eD8bFQAAAABJRU5ErkJggg==)
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,iVBORw0KGgoAAAANSUhEUgAAADcAAAARCAYAAAB5LjRtAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAPUJuPDwAAAaJJREFUeNpjYBj64D8U/wLio0CsgkthFhB3DFJPdEDdhwswQeXPYZPUA+LjgzyWjkLdiQ/8wKXRAEt048LUBvZAfBjquG9AvAaIldDUGEPV4DPjILqgAdRzxIBQIJ5NZY+5AfEVIDaFJi8WIE4G4htALI6m9jDUk+hAEuoH9ABh6ALiHCIcIQ41nIOEzE4MOIPNUdCA7EITy8NSLqgB8RaoBzHADiC2JcIRm9CSLrU89wdPIYFeQFgC8V60GNsGxHy4DP8ExGwEHJABxLVkFNPEgLs4kpo8NP8hAzaoe2EA5DENckIO2ZKT0LxAC8+Bkt99aIHABMU+0Fj7hUX9LwIFH0meA5VAjiRUqOSUsiCP7YeWliC8ClohfyPgOYIAX7IMhUY9ua0HSgAHNMXgS5YEwW4gtsaRoW+QWIhQ03Og1NJMoEAhCHBVBQHYKkU6eq4ViKXRxHKwVA94Aa5KfDkQJ9LBc6CYCELKGtLQktkPi1pclThecBxLu+0lEAvSoc3oAi1M/kDz03IcbUhCzS+cYLg0nPFW1IO1ywPKZ2mkaAAAiPpuZM/W44UAAACIdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1vPig8L21vPjxtbj43PC9tbj48bW8+KzwvbW8+PG1uPjk8L21uPjxtc3VwPjxtbz4pPC9tbz48bW4+MjwvbW4+PC9tc3VwPjwvbWF0aD6YBMINAAAAAElFTkSuQmCC)
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.
How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
![open parentheses 11 cubed close parentheses plus 5 cubed](data:image/png;base64,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)
How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
![open parentheses 11 cubed close parentheses plus 5 cubed](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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)
We use identities to speed up the process of multiplication and simplification. There are some basic polynomial identities that you need to by heart.
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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)
We use identities to speed up the process of multiplication and simplification. There are some basic polynomial identities that you need to by heart.
How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
![x cubed minus 216](data:image/png;base64,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)
How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
![x cubed minus 216](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEIAAAARCAYAAABpTnqxAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAbFJREFUeNpjYCAd/IfiX0B8AYjdGEYBgwYQPxwNBgYGJiB+N9IDQRiIpwBx4kgOBFg5EUsj862BeA0Qf0Iqi6LxqFcD4lqoOnzAFIhXQc39AcSbgNieUsfyAXErEKfRICAOAnEkEPNA+VpAfBQqhg0shrrjPx4z06AeV0NyPyhwD1PL0T/olArlgfgSESkVGwAF5BliLUoG4g4s4s1QOWzAlhQL6BDouAJiJp7UhBWcA2JxJH4itEDEVj6AHLUDGlP0AJbQ7EFOQNwAYklSLPMA4j4o2wWI9w6SwpkDiE9CC1FyAuIHtGxYB8TfoAXwGQIFMMNuaEl6AVpFUqN2wYcJAUEg3kBkC/Y/HnFQavcCYhZo+wcUqLeAOAuXYQXQENMbBClBCRoIKiQEPDYAqi6lsYgbAPFTfPV3H6mFC42a77OBmIvEFIgNbIOmAmzgF7bQ3wS1mAeah4QHKBDEoQ0fFjKyIjYASv7hOAL7JLKAKDTUkD3uA22oDATYAnUkA5UCgg3aSEtGClxzaLvEBVnROhx5aDm0JhmoJjyxhSsx6kShWe0LEP+BBoztaL8ZDQAAWQttjRgWwXQAAAB9dEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1zdXA+PG1pPng8L21pPjxtbj4zPC9tbj48L21zdXA+PG1vPiYjeDIyMTI7PC9tbz48bW4+MjE2PC9tbj48L21hdGg+XmTPWQAAAABJRU5ErkJggg==)
Use polynomial identities to multiply the expressions ?
103 × 97
Use polynomial identities to multiply the expressions ?
103 × 97
How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
![open parentheses 9 m to the power of 4 close parentheses minus open parentheses 25 n to the power of 6 close parentheses](data:image/png;base64,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)
How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
![open parentheses 9 m to the power of 4 close parentheses minus open parentheses 25 n to the power of 6 close parentheses](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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)
We use polynomial identities to reduce the time and space while solving polynomial expressions and equations.
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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)
We use polynomial identities to reduce the time and space while solving polynomial expressions and equations.