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

asked by guest
on Apr 06, 2025 at 7:59 am



You asked:

Evaluate the expression: 1x7(x+8)7−156(x+8)8\frac{1 x}{7} {\left( x + 8 \right)}^{7} - \frac{1}{56} {\left( x + 8 \right)}^{8}

MathBot Answer:

Evaluated



1x7(x+8)7−156(x+8)8=x(x+8)77−(x+8)856\displaystyle \frac{1 x}{7} {\left( x + 8 \right)}^{7} - \frac{1}{56} {\left( x + 8 \right)}^{8} = \frac{x \left(x + 8\right)^{7}}{7} - \frac{\left(x + 8\right)^{8}}{56}

Expanded

1x7(x+8)7−156(x+8)8=x88+48x77+160x6+2048x5+15360x4+65536x3+131072x2−20971527\frac{1 x}{7} {\left( x + 8 \right)}^{7} - \frac{1}{56} {\left( x + 8 \right)}^{8} = \frac{x^{8}}{8} + \frac{48 x^{7}}{7} + 160 x^{6} + 2048 x^{5} + 15360 x^{4} + 65536 x^{3} + 131072 x^{2} - \frac{2097152}{7}

Factored

1x7(x+8)7−156(x+8)8=(7x−8)(x+8)756\frac{1 x}{7} {\left( x + 8 \right)}^{7} - \frac{1}{56} {\left( x + 8 \right)}^{8} = \frac{\left(7 x - 8\right) \left(x + 8\right)^{7}}{56}

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