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

asked by guest
on Apr 06, 2025 at 7:58 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=x7(x+8)77−(x+8)856\displaystyle \frac{1}{7} {\left( x \left(x + 8\right) \right)}^{7} - \frac{1}{56} {\left( x + 8 \right)}^{8} = \frac{x^{7} \left(x + 8\right)^{7}}{7} - \frac{\left(x + 8\right)^{8}}{56}

Expanded

17(x(x+8))7−156(x+8)8=x147+8x13+192x12+2560x11+20480x10+98304x9+14680063x856+299592x7−32x6−512x5−5120x4−32768x3−131072x2−2097152x7−20971527\frac{1}{7} {\left( x \left(x + 8\right) \right)}^{7} - \frac{1}{56} {\left( x + 8 \right)}^{8} = \frac{x^{14}}{7} + 8 x^{13} + 192 x^{12} + 2560 x^{11} + 20480 x^{10} + 98304 x^{9} + \frac{14680063 x^{8}}{56} + 299592 x^{7} - 32 x^{6} - 512 x^{5} - 5120 x^{4} - 32768 x^{3} - 131072 x^{2} - \frac{2097152 x}{7} - \frac{2097152}{7}

Factored

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

+ Submit Question