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

asked by guest
on Apr 06, 2025 at 7:57 am



You asked:

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

MathBot Answer:

Evaluated



17(x(x+8))7−156(x+8)8=−156(x+8)8+17x7(x+8)7\displaystyle \frac{1}{7 {\left( x \left(x + 8\right) \right)}^{7}} - \frac{1}{56 {\left( x + 8 \right)}^{8}} = - \frac{1}{56 \left(x + 8\right)^{8}} + \frac{1}{7 x^{7} \left(x + 8\right)^{7}}

Expanded

17(x(x+8))7−156(x+8)8=−156x8+3584x7+100352x6+1605632x5+16056320x4+102760448x3+411041792x2+939524096x+939524096+17x14+392x13+9408x12+125440x11+1003520x10+4816896x9+12845056x8+14680064x7\frac{1}{7 {\left( x \left(x + 8\right) \right)}^{7}} - \frac{1}{56 {\left( x + 8 \right)}^{8}} = - \frac{1}{56 x^{8} + 3584 x^{7} + 100352 x^{6} + 1605632 x^{5} + 16056320 x^{4} + 102760448 x^{3} + 411041792 x^{2} + 939524096 x + 939524096} + \frac{1}{7 x^{14} + 392 x^{13} + 9408 x^{12} + 125440 x^{11} + 1003520 x^{10} + 4816896 x^{9} + 12845056 x^{8} + 14680064 x^{7}}

Factored

17(x(x+8))7−156(x+8)8=−x7−8x−6456x7(x+8)8\frac{1}{7 {\left( x \left(x + 8\right) \right)}^{7}} - \frac{1}{56 {\left( x + 8 \right)}^{8}} = - \frac{x^{7} - 8 x - 64}{56 x^{7} \left(x + 8\right)^{8}}

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