To simplify the expression \(122(x+1)^5\), we can use the binomial expansion formula. However, since you're looking for a simplified version, it is sufficient to express it in a more manageable form without fully expanding it.
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Leave it in factored form: \[ 122(x+1)^5 \] This is already a simplified version, as it clearly shows the coefficient and the factored expression.
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If you're looking for a binomial expansion: Using the binomial theorem for expansion: \[ (x + 1)^5 = \sum_{k=0}^{5} \binom{5}{k} x^k 1^{5-k} = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1 \] Therefore, \[ 122(x + 1)^5 = 122(x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1) \] Expanding this out gives: \[ 122x^5 + 610x^4 + 1220x^3 + 1220x^2 + 610x + 122 \]
In summary, the expression can be left as \(122(x+1)^5\) for a compact form, or expanded fully to find each individual term contributed to the polynomial. If you need something specific, please clarify!
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