Mathematics
Grade10
Easy
Question
Expand using the binomial theorem.
![left parenthesis 1 plus x right parenthesis squared](data:image/png;base64,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)
Hint:
Expand using binomial expansion.
The correct answer is: ![1 plus 2 x plus x squared](data:image/png;base64,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)
STEP BY STEP SOLUTION
![open parentheses 1 plus space x close parentheses squared
E x p a n d i n g space u sin g space b i n o m i a l space e x p a n s i o n space
scriptbase C subscript 0 end scriptbase presuperscript 2 space 1 squared space x to the power of 0 space end exponent space plus space scriptbase C subscript 1 space 1 to the power of 1 space x to the power of 1 space plus scriptbase C subscript 2 space 1 to the power of 0 space x squared end scriptbase presuperscript 2 end scriptbase presuperscript 2](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAASkAAABOCAYAAAB8H+DUAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAyCPPDHgAACkpJREFUeNrtnQ9kH0kUx0dERFSIqoioUlF1qsI5FRVV6pyIiKNOnFMV6lTVqRIRVadKxalTcZyqqqoQFaeiSlVExTmq6pyoUKdOVZSIqogIv5t3v/frbec3szv777cz+/t+eCT7292ZeW/m7ZuZ3RkhykmFZVvKspQ+AQAADtIi5ayU51AFAOWAGvQ1j/J7jfMcxRZMC4D/HJbyu4f5Xua8mzgmZQnmBcB/qLH3a44fkHJJygtH8/25lKeG33q4XPthXgD8pp8bs467Us6I6kC0qzxlZ6U61wV2VAAAz5mWci7inCROqlGO7bz4dCyNHNNDKZ0wLQDl4JGUQcec1LjQD+Jf4d+CDEh5EvifHNRBmBWA8vBeSpuDkRS9OtAd+P+0lBnNeW1chmC6qgAAPGYnJ4eT1jl8JeU6/31CiZZUtmFGAOCkbM6Jkrg8FtXXCGh2cTecFADo7rkUSRE/sAMKexdK7e4BAEoGRStHHXRSlKf73OUbCzlvIKIrCADwHBdfQaAXMB9I6ZCyS8qzkO7eOS4DAKCkhL3MWYST2iOqrxEEndKwqL5YqkP3MicAoGTQd3uHDY6mkdP5NL40L6VX89usqM74BQn7LAYAUCLK+oExAKBEfC/8WqqFxqHOwGwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACgutuv7qNiWniuxdMybWryvulxeSqO6TKLc10vS1nqjgv6S0WfcHcT0DRl+tPiGJxUMl1mca7rZSlT3Slaf6kZlXKvZMqkMs2iTkGX0EE5uCxlIuR3273w6D5TUn6U8pa7kIuifjfhFj5njbuTFMXt0+TpoqhubXWbQ8x1Ud0QVIVW8LwhZYPTpKWHZzRlUssZJw1aKZRWX3gXkYatbtXj+1lXm8K8flfF8P9JKa84X0tS9hrykqYMNnZNq2Na9PCWlA+cxh0p7Yb7d7PN1zhPQ/x7l6guO01p0Pr3kxH5s6mLNm2kRjfrlfL/WlQ3E/GpLU1xvne4fk1Y6MHWbrZ50DLHT4owbPbCm+PGMsGVpYUrjPoEWuAKVjtHl/4cF+A2G5rO62UldChGWuT80N+drJCK4Z6jCdJo5cY/wX+TXGBDjibUrXqclkkeidndq7CDmg5UzNOcV5W0ZbCxaxodd3E3ImjHWVG/PPQc25f0NcbloLL/zQ2YyvgNH9/L6XSH5M+mLtq2kU4uQ82On0n5y6O2RA7qpgjfnEW9fxy72eTByKrQD5oHV8m02QtvlQ2jGi64o8sYZzjIncCTMHgv3ZpR5H2DywtfMjzhVkX9Kp/qsThpXDWk0WOh216L45ts8LhO6rjmyarb5ittGaLsmlbH0+w0hRJdrmru/0SjqzfcwHTHewz5s62LYXYUShkmNU5EbfSutqVlzk+c+hzHbjZ50NLCYZoNYXvhtXBDU2lXFEtRz4ByzpISopry1KpJ4x/u7kXlRT0WJ423hvJ+sNDtpuXxUa4kYzGdlM15eZShXeOkkuq4hbug7Zo0NjT37zCk22GRn82YdTFMB+o5G9z1CR57L/QzYS62pZMc5Y1Y1oU4drPNg5Yjwn5bqLC98I6w0lTUbafU6UtdAcLuFTzeb+ja6K5Xj9mmYVpL3XS9zTmm47s4GliRciBDJ5VHGXTbieWt47j6jLrepi7G0ZOuN7LsSVuq0cO2WNQ8/I9kbLcBC71+DBlvWZwXtRfeGPc3VS5wV6PGO819n1veSz3+tdDvJKO7Xj2WRxq255yKuHZSo5M0TiqPMqh2TaPjEU23pdaQrya4n21+bOqirZ5MZfClLamREI0zfVeQ3eq4wYNeYdjshae7TxsXtkcZI2hXxkrua+41bsjruNJF0inprqb/q15rm8aIYYD4ruH6ID+L+tmLL7jrNR7RddjO0EmlKYOtXdPomMZoHmp0QBHlQeW6M4b72RxX07Wpi2H3V6OCPyzam6ttSYUCl28ztFuSPHxkXtRvFxXEdi+8eR4cqw289fIxVdk01forF4b6zvc0BZ03DF6qxztYIf2B8HOBjTcUca1tGjRYuRZIo58rwhtRP72scpkHMltYj/T/TEjaNcYNYXBSJ5WmDLZ2TaPjVs7LsJLGVMJ6YZsfm7ooLOxVY4WjCLpfF0fEg560JfVBuqJxno2yWx3rhr50hT297V546xzZkHJ3eEDQNGU7xRHQJX4SrCnnrmsG40zHuzmPNJVJW3MdN5ynHouTBkUirzm6oSfflxxqR30aQBX1EV+3FDCmLo2azne4ovVk6KTSlGGNr7WxaxodD3LDoPy9NDjBOPezzU9UXQy7vy5Kesp6WlGihDbH29JGoP4tKpFQo+2WC22cYFL2CL84JPx/+7gMZciDoutis7WlhjHET4kyQk+UXwKRDYXCy4YnDcoA0JYc5RQPgpWR2ic3NLW7yV2xQygDQFsCAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADKSXArMXorvA8qAQC4CH34e1bo1zcCAABn2IIKAACuQms9LUEN6GYD4CI93Fj2QxXoZgPgGrQJw4KI3moKoJuNELdJ8kkrZr5kGXYggqKlVDo9caa0IuQLz+7tezc7r/rqtD/wJcTNI58DXCF3s+j2Mmsk5KB8WYyutuFFxbN7+9zNbkR9ddof+BLiZpnP38SnmxHQms0PHIgag+JDRO7jvX3sZjeyvjrnD3yZSco6n+oOs7VdZ0FzOSlfutmNqq/O+QPbEJd+n+ZxAlqGlnYfoW11uho0/pBHKK5rBNseOYiibVIWJxW3m12U3htRX53r8tqGuBf5vMGAJ98rqvuM3U6ZB5vxh7xCcfXJ1OpRJFW0TcrkpOJ0s4vUe9711bkur22IOyHlZoHdhjxDcbWPf4yN5HrjKtomvjipSsn0nld9dbbLaxPikmd9xR67KMMkmfGijRmvaY5fEZ9u2kgzI4scpu/hfviQA43LdZskKautTVx1Ui7oPUl9tdW7kzPLNiHuTxzGigINk3TGi6ZQuwP/0+6qM5rz6F0T2i2WNmU870E3xQWbJLWLrU2ymuWslFDvSeqrjd59nFn+D9pCuc8BwySBtq6+zn+fkPKkwQ8A2KR4m1Sg98LbQq7QAN2W5w37MffbabZkd4Oj0jyeSrBJMXaA3h2F9qV/77lhKDynKdrDBXSlYZPibVKB3gtvC7lDW3N3xDg/zXdFWRvmqJT7HOaOlcRJJbFJmu/gfLdJpSC9p/0OrkxtIXduiep7ITak/a4oS8PQi2gPuFLtkvKswSFuxRGbEGm+g/PdJpUC9V7rJib5Dq5MbSF39onqLMKk+P9t2naOkshoJwLnpv2uKCvD0NTsQ8UQw9xYy+Ck4tgkbZ58t0nFAb0TW02m94ZDoeod7pOT8jY4dFTfz0j6XVGWg8w0djAvpVfz26yoznI0k02SVnzYJDu9x/kODnov4Km1LYDL9gH5ghVWHcPn7+DgpEDWYIVVB8nzuyIAJ+VbBOXLCqtNRV7fwQE4Kd/waYXVpiOP7+BAeufk5TdZ0Hnz8i+A6WY7TSn0RAAABQ50RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bXN1cD48bWZlbmNlZD48bXJvdz48bW4+MTwvbW4+PG1vPis8L21vPjxtbz4mI3hBMDs8L21vPjxtaT54PC9taT48L21yb3c+PC9tZmVuY2VkPjxtbj4yPC9tbj48L21zdXA+PG1zcGFjZSBsaW5lYnJlYWs9Im5ld2xpbmUiLz48bWk+RTwvbWk+PG1pPng8L21pPjxtaT5wPC9taT48bWk+YTwvbWk+PG1pPm48L21pPjxtaT5kPC9taT48bWk+aTwvbWk+PG1pPm48L21pPjxtaT5nPC9taT48bW8+JiN4QTA7PC9tbz48bWk+dTwvbWk+PG1pPnNpbjwvbWk+PG1pPmc8L21pPjxtbz4mI3hBMDs8L21vPjxtaT5iPC9taT48bWk+aTwvbWk+PG1pPm48L21pPjxtaT5vPC9taT48bWk+bTwvbWk+PG1pPmk8L21pPjxtaT5hPC9taT48bWk+bDwvbWk+PG1vPiYjeEEwOzwvbW8+PG1pPmU8L21pPjxtaT54PC9taT48bWk+cDwvbWk+PG1pPmE8L21pPjxtaT5uPC9taT48bWk+czwvbWk+PG1pPmk8L21pPjxtaT5vPC9taT48bWk+bjwvbWk+PG1vPiYjeEEwOzwvbW8+PG1zcGFjZSBsaW5lYnJlYWs9Im5ld2xpbmUiLz48bW11bHRpc2NyaXB0cz48bXN1Yj48bWk+QzwvbWk+PG1uPjA8L21uPjwvbXN1Yj48bXByZXNjcmlwdHMvPjxub25lLz48bW4+MjwvbW4+PC9tbXVsdGlzY3JpcHRzPjxtbz4mI3hBMDs8L21vPjxtc3VwPjxtbj4xPC9tbj48bW4+MjwvbW4+PC9tc3VwPjxtbz4mI3hBMDs8L21vPjxtc3VwPjxtaT54PC9taT48bXJvdz48bW4+MDwvbW4+PG1vPiYjeEEwOzwvbW8+PC9tcm93PjwvbXN1cD48bW8+JiN4QTA7PC9tbz48bW8+KzwvbW8+PG1vPiYjeEEwOzwvbW8+PG1tdWx0aXNjcmlwdHM+PG1yb3c+PG1zdWI+PG1pPkM8L21pPjxtbj4xPC9tbj48L21zdWI+PG1vPiYjeEEwOzwvbW8+PG1zdXA+PG1uPjE8L21uPjxtbj4xPC9tbj48L21zdXA+PG1vPiYjeEEwOzwvbW8+PG1zdXA+PG1pPng8L21pPjxtbj4xPC9tbj48L21zdXA+PG1vPiYjeEEwOzwvbW8+PG1vPis8L21vPjxtbXVsdGlzY3JpcHRzPjxtcm93Pjxtc3ViPjxtaT5DPC9taT48bW4+MjwvbW4+PC9tc3ViPjxtbz4mI3hBMDs8L21vPjxtc3VwPjxtbj4xPC9tbj48bW4+MDwvbW4+PC9tc3VwPjxtbz4mI3hBMDs8L21vPjxtc3VwPjxtaT54PC9taT48bW4+MjwvbW4+PC9tc3VwPjwvbXJvdz48bXByZXNjcmlwdHMvPjxub25lLz48bW4+MjwvbW4+PC9tbXVsdGlzY3JpcHRzPjwvbXJvdz48bXByZXNjcmlwdHMvPjxub25lLz48bW4+MjwvbW4+PC9tbXVsdGlzY3JpcHRzPjxtc3BhY2UgbGluZWJyZWFrPSJuZXdsaW5lIi8+PC9tYXRoPvm7S6UAAAAASUVORK5CYII=)
![1 plus 2 x plus x squared](data:image/png;base64,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)
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