Question
Use binomial theorem to expand
.
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:
Here, the value of n=4. So, the combination permutation we would use is .
We would have 4+1=5 terms in the expansion of the expression
.
Step 2 of 2:
Substitute the values of
in the binomial expansion:
![left parenthesis x minus 3 right parenthesis to the power of 4 equals 4 C subscript 0 x to the power of 4 plus 4 C subscript 1 left parenthesis x right parenthesis cubed left parenthesis negative 3 right parenthesis plus 4 C subscript 2 left parenthesis x right parenthesis squared left parenthesis negative 3 right parenthesis squared plus 4 C subscript 3 left parenthesis x right parenthesis left parenthesis negative 3 right parenthesis cubed plus 4 C subscript 4 left parenthesis negative 3 right parenthesis to the power of 4](data:image/png;base64,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)
![equals x to the power of 4 plus 4 left parenthesis x right parenthesis cubed left parenthesis negative 3 right parenthesis plus 6 x squared left parenthesis 9 right parenthesis plus 4 left parenthesis x right parenthesis left parenthesis negative 27 right parenthesis plus 1 left parenthesis negative 3 right parenthesis to the power of 4](data:image/png;base64,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)
![equals x to the power of 4 minus 12 x cubed plus 54 x squared minus 108 x plus 81](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPMAAAARCAYAAAAIepq2AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAA7BJREFUeNrtWl+EVFEcPlbGyoqsJD0sa2WtNS/pYY1kyNqHJEMPY+3DWpIkq5ce0lOihyRJJKuHlchIshJZ6SFZ1koPK9FDesi+zMNaGWO5/X7mG12nc2fOOfee+2/ux8fOvTtzz+/fOd/vnCtE8pgneiJf8MA28QtxNsf2fSJOiAIDj2kkg5djGyeJP3Nq2xDxCnGrSOXBxmHiZ+LxnBczJ3wz57FsFek82GgQZ3yyLY8YJT4iLuY4jmeIH4t0HlzcIC5IPZgrnCDeQu+qQgUTy66vx52PsK9ccNy3qtgL5yL09zG0SeMJxo9xiPiYuAE+wTUZB4kPiXtQE++gDJOGybh0/BErbJLQFqvESz1+n1eVOnEEn6eQoPUIns0JdQfPd+FDU7CN2xH5mpNqDQXtEv3ix1gnnpcmrHXF/60gHgeIJeJdFH/SMBmXjj8SL+40PWOM+DWhntJz6DNesZYi8DcX8NuA1S/u+F3EqibjgWJCbin2M9opyDebcTmvmSXMKjJu415WijmoAG3sO03cTEExV3yrlRcyflzIkymZ8LlFUh39VXHPjz2fAusWza8I89g2PrrjMv59T4O9wMcUR32fF7EJlKWVeQZS29a+rp+6/c9YwsVcgtIY0/iuiX2uWyQde5uwT2XzjnSNV/BrUpzvRZjHtvExGVecNSPmiPfx99mA3iXNUn4Y/UolIftMipml2C5WyuvS7O4HrzJXNZ+Rtfjt9/iOLFXLuNbGXslvKCcXfjApNpNxxVrMjPeic2TBO26jEQQxjFIwMZ7Pvl+L/m9spck+3jQ5KTo7nN8U8resUBlejuK3r9kqsSp5jn6/u5Kz337AR2H9YGunzbhik9mMZcwyZZEe9Bv3OAp5ImH7wsy4s+L/M98NhU1ejuK3EyCzhyWZ/SrAHu6tPzjwg24cbcYV28rcPbdliVLPSDHzavZUdM77krYvbJBahpNz1uPXgCRWTWyNHn4Rfe6F9YNnGS/de86LmVe3NygK7t82I5BprpOBNzleQq6mwb4wQZqGPLN9RhbjV8NELOOZVITbAaprCj1q1H7QjaPJuGIr5iPYiPEbzYf3qylPhjWhd8wSl30m8ox3PYfAORRyzfIZWY2fgBxdFv9euripaDdqKJyqz2dV+OyyAz/oxlF3XLEVcwnJpXoF7UWADIozCXpJSx0Jmkb7+GWJ79gAakJdnLJMtCzHj8EblyuQpX9E5+WYkQCfbaEPbqHgL6TAD/3GZeqPAgUKZBl/AV32jP370eqVAAABGXRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtbz49PC9tbz48bXN1cD48bWk+eDwvbWk+PG1uPjQ8L21uPjwvbXN1cD48bW8+JiN4MjIxMjs8L21vPjxtbj4xMjwvbW4+PG1zdXA+PG1pPng8L21pPjxtbj4zPC9tbj48L21zdXA+PG1vPis8L21vPjxtbj41NDwvbW4+PG1zdXA+PG1pPng8L21pPjxtbj4yPC9tbj48L21zdXA+PG1vPiYjeDIyMTI7PC9tbz48bW4+MTA4PC9tbj48bWk+eDwvbWk+PG1vPis8L21vPjxtbj44MTwvbW4+PC9tYXRoPh/5ohoAAAAASUVORK5CYII=)
Thus, the expansion is:![left parenthesis x minus 3 right parenthesis to the power of 4 equals x to the power of 4 minus 12 x cubed plus 54 x squared minus 108 x plus 81](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAASsAAAASCAYAAAADpvhlAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAABMpJREFUeNrtXFFkHFEUfVatqAgVFdGPEFEREaH6ERERKqqqIuQjIqpCVEVFf/pR+aqyqioiSlT0I6rUqqqoEBEVESGi+hEVoqoflZ98RNRaYXqvvSvT1zcz783Mm/d2ModDdnZ33rv3vnvfvXfehrEMujEGdFImk0MsA78CB1Ms3yawLVvGGdIeHDppsTsp1nc78GdKZcsBHwB3M7eyD2iYgsXzK9AcayE4XAJuAa+kPFihQx+l3C9KWWiwC13kXLZjk+Zqe3AoAntcZUUa0QicB95LsV/0A79k4cG+INBtcPwB4GfgH9rJ9oGz5BBuXANuWB4cHgPHXa91zucqcIZVekci9JJujtlZj2kshnGrfZ1xTXI5PvTD7Rj13Ux+0WrQfogG4CvgNnGBrvG4CJwDnpAPrdDmbRoq8wrURzcZxSTWgcPAPDevFcFnNyhomQgOURxNB5aAkz73x6xgFFhPrzvI1qMxjI0O84zG16FDVaCMezHpGp1mmQKWTgTZD7EGvMMF5DXB5xbJHhfIjwoU3ExDZV6B+ngOnLI04zsWXHvI/u2tJRkcknI8nWO0AL8Z6uk4GnWGGcdEDPpupiy/wYI1MkJZCY9ZwYbD2yFH2bTp9RZmXp73x+ylT3B9gokb7k/pPd3A9Pu74HqPx86iOziE1YdtwcorwISRD9fNjgXBqte1JpyI9sNA1W7JhoYl/KBH26TIXTtxZdDVoPBLk1+r2Ed2XlL3P+bKLzfwsW2T6zU2U+c1G66JxsG+1S3B+3mPjEtGkY4E/RBGH7YFqx6fsl9Gvqqeqv2HFsPBKk+ZYovEd1XkSzJL9xrjyMM38dohd22Oqg63nV9o8msVnajMK/D+pz5fugl8SX/fCMho4u71TPt8tmwoOCSpDx3Bqo76Bb2G5FMJVmXalDDTecTtzm4UuDaGkyL7nSr4QBddQ2Kv8rdHxRSHHlR8TGVekYIVYpVVHuFih75RMeCE2aXwGMIQOVV/iGClGyr6YAnoiyno9SMLPnFuk3zYlMWHKTPUEmgXOMKmoi5qyX6nkqU8ZpVvWaXfVs3EUG8HTHzUJym/DjOv0GUgowynHHBzHahn4qcGQWWg7sVlSh9RglUrBao2w/JFyXoH2f9nnrYFMjkpst+hh2/WcWXgBw95sLe1rkEPsnYMMy/f+6/6lAXVczqYMo4aMGLJo+diKn03rY8wiwezkdesct7FtHxOzOtBdeOpNfsVqWQTBe5igJ/4vRdVD04E/5V5T/noAu7Gn2iRY5azE0ParAKMyPuC61M056RhWh9hFg82Ud9TOWWDfFGCVSeVD2HHqEX7DdNGw+MNF2T2PLLmDuoRxa0HWTuqzEvq/qJDoZdZpbHpFgIPoy1pMham9yPkVDlKE38A7wo+yx8KTQJJ6yOuxb7M5B7DJyWfSvnQQ2shR9nFATlvmDFq1X6MyqVpdnao8omgHB6mwDDg0tkA6ey+Bj3I2lF2Xkr333LVlnlaLKIj8e880tKo6CPHKhHXSYk8vH5uoxMm9KGyaPxKH5kSyUb5RiirxgbzEWWH10M6Ui3bD4EPRhbJL/DnaAtM/GQUdbZLfagSBbQhC/QQNC9VfdT8D5kzZMhwjoBpmc3/Igb7VJOZmTJkOH/4C5hD78zxS4n2AAABaXRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtbz4oPC9tbz48bWk+eDwvbWk+PG1vPiYjeDIyMTI7PC9tbz48bW4+MzwvbW4+PG1zdXA+PG1vPik8L21vPjxtbj40PC9tbj48L21zdXA+PG1vPj08L21vPjxtc3VwPjxtaT54PC9taT48bW4+NDwvbW4+PC9tc3VwPjxtbz4mI3gyMjEyOzwvbW8+PG1uPjEyPC9tbj48bXN1cD48bWk+eDwvbWk+PG1uPjM8L21uPjwvbXN1cD48bW8+KzwvbW8+PG1uPjU0PC9tbj48bXN1cD48bWk+eDwvbWk+PG1uPjI8L21uPjwvbXN1cD48bW8+JiN4MjIxMjs8L21vPjxtbj4xMDg8L21uPjxtaT54PC9taT48bW8+KzwvbW8+PG1uPjgxPC9tbj48L21hdGg+OYGWIwAAAABJRU5ErkJggg==)
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
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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,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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 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.
Use polynomial identities to factor the polynomials or simplify the expressions :
![8 x cubed plus y to the power of 9](data:image/png;base64,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)
Use polynomial identities to factor the polynomials or simplify the expressions :
![8 x cubed plus y to the power of 9](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 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 polynomial identities to factor the polynomials or simplify the expressions :
![x to the power of 9 minus 8](data:image/png;base64,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)
Use polynomial identities to factor the polynomials or simplify the expressions :
![x to the power of 9 minus 8](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,iVBORw0KGgoAAAANSUhEUgAAADcAAAASCAYAAAD/ukbDAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAPUJuPDwAAAaBJREFUeNpjYBj64D8WjBVkAXHHIPVEB9R92DxHEOgB8fFBHktHoe4k2XMgjQaD3HPGQHwYi+d+AfEFII7HpskA6rmhAA5DPYkMmKBie4E4Fl1DFxDn0DDDUxPk4SkXhIH4CrrgDiC2xaI4GYdBzVA5anpuLhCHYxEvAOJWJL4lNIawATYgvoUu+AkqgQ2cA2JxJH4iEE+hQczFQ1MQMuCCOlYYzQOfsOjngwYQRr77g8dSDyDug7Jd8IQapZ7zAuJVaGL1QFyLRe0vNPP/QEv6SGwG/yFg8W4gtoeWSMJkVKrEVLLo+UUUiO8CMQcBzxEE+JIlLN3/wlLHULtA+YbE7oPaiy1ffSLFAaCYscYhBxJfA7UsksaeAxXzSlB8F1rEowNLUrMGrqoAZMkmaMbmAeIzRCRLSjy3EIj9gHgptvoKCnKwFDx4AbZKHJTmt6F5xgeIF9PQcwXQEu8SiZU4QXAcKU+B0vU6IJbGom45tASlBQiABoYfCc0vosBgaDj7EXDDUTILNTDIGOAuzzZogYGrXEgbqp1OHSDeQk0DAXAUZOWOXYrsAAAAiHRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtbz4oPC9tbz48bWk+eDwvbWk+PG1vPis8L21vPjxtaT55PC9taT48bXN1cD48bW8+KTwvbW8+PG1uPjU8L21uPjwvbXN1cD48L21hdGg+rS+pUgAAAABJRU5ErkJggg==)
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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)
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,iVBORw0KGgoAAAANSUhEUgAAAD8AAAARCAYAAABq+XSZAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAARVJREFUeNpjYKAN+A/Fv4D4AhC7MQwcGFC3aADxQ4bBAejuFiYgfjdIPE9XtwgD8RQgThwEHifoFjUgroXmDWzAGojXAPEnpDwUTSCvxdLIM1R3y2IgToMqxAYOAnEkEPNA+VpAfBQqhg3wAXEr1ExqA5q55T8JjpAH4ksE1PwgsXQmF1DFLaQ6AJ+BtkB8hk6ep4pbSHGAJTS5YctjIIfsgMYIPTxPFbcQ6wAOID4JLXyo2SghB1DNLcQ4QBCIN1ChxfSfCEwvtxDleSWoZSo0ao6SAqjulv8EmoizgZiLhm1xUpqrVHcLLgeIA/EqIGahcUeEGEAzt+BywBZoaDMMAs9T3S2EChtKCiVadVUHg1uGHgAAfxluRSdQrX8AAACMdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1zdXA+PG1uPjEyPC9tbj48bW4+MzwvbW4+PC9tc3VwPjxtbz4rPC9tbz48bXN1cD48bW4+MjwvbW4+PG1uPjM8L21uPjwvbXN1cD48L21hdGg+PSDROwAAAABJRU5ErkJggg==)
How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
![12 cubed plus 2 cubed](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAD8AAAARCAYAAABq+XSZAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAARVJREFUeNpjYKAN+A/Fv4D4AhC7MQwcGFC3aADxQ4bBAejuFiYgfjdIPE9XtwgD8RQgThwEHifoFjUgroXmDWzAGojXAPEnpDwUTSCvxdLIM1R3y2IgToMqxAYOAnEkEPNA+VpAfBQqhg3wAXEr1ExqA5q55T8JjpAH4ksE1PwgsXQmF1DFLaQ6AJ+BtkB8hk6ep4pbSHGAJTS5YctjIIfsgMYIPTxPFbcQ6wAOID4JLXyo2SghB1DNLcQ4QBCIN1ChxfSfCEwvtxDleSWoZSo0ao6SAqjulv8EmoizgZiLhm1xUpqrVHcLLgeIA/EqIGahcUeEGEAzt+BywBZoaDMMAs9T3S2EChtKCiVadVUHg1uGHgAAfxluRSdQrX8AAACMdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1zdXA+PG1uPjEyPC9tbj48bW4+MzwvbW4+PC9tc3VwPjxtbz4rPC9tbz48bXN1cD48bW4+MjwvbW4+PG1uPjM8L21uPjwvbXN1cD48L21hdGg+PSDROwAAAABJRU5ErkJggg==)
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,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)
The answer cam also be found by expanding the formula of 5Cr .