1/7x * (x+8)^7 - 1/56 * (x+8)^8

asked by guest
on Apr 06, 2025 at 7:58 am



You asked:

Evaluate the expression: 17x(x+8)7−156(x+8)8\frac{1}{7 x} {\left( x + 8 \right)}^{7} - \frac{1}{56} {\left( x + 8 \right)}^{8}

MathBot Answer:

Evaluated



17x(x+8)7−156(x+8)8=−(x+8)856+(x+8)77x\displaystyle \frac{1}{7 x} {\left( x + 8 \right)}^{7} - \frac{1}{56} {\left( x + 8 \right)}^{8} = - \frac{\left(x + 8\right)^{8}}{56} + \frac{\left(x + 8\right)^{7}}{7 x}

Expanded

17x(x+8)7−156(x+8)8=−x856−8x77−223x67−504x5−4928x4−30208x3−110592x2−1409024x7−2621447+20971527x\frac{1}{7 x} {\left( x + 8 \right)}^{7} - \frac{1}{56} {\left( x + 8 \right)}^{8} = - \frac{x^{8}}{56} - \frac{8 x^{7}}{7} - \frac{223 x^{6}}{7} - 504 x^{5} - 4928 x^{4} - 30208 x^{3} - 110592 x^{2} - \frac{1409024 x}{7} - \frac{262144}{7} + \frac{2097152}{7 x}

Factored

17x(x+8)7−156(x+8)8=−(x+8)7(x2+8x−8)56x\frac{1}{7 x} {\left( x + 8 \right)}^{7} - \frac{1}{56} {\left( x + 8 \right)}^{8} = - \frac{\left(x + 8\right)^{7} \left(x^{2} + 8 x - 8\right)}{56 x}

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