Solve (x-1/8)(x^6+1/64x^3+1/4096)

$$( x - \frac { 1 } { 8 } ) ( x ^ { 6 } + \frac { 1 } { 64 } x ^ { 3 } + \frac { 1 } { 4096 } )$$

Evaluate

$$\frac{\left(8x-1\right)\left(4096x^{6}+64x^{3}+1\right)}{32768}$$

Solution Steps

Use the distributive property to multiply x-\frac{1}{8} by x^{6}+\frac{1}{64}x^{3}+\frac{1}{4096}.

$$x^{7}+\frac{1}{64}x^{4}+\frac{1}{4096}x-\frac{1}{8}x^{6}-\frac{1}{512}x^{3}-\frac{1}{32768}$$

Expand

$$x^{7}-\frac{x^{6}}{8}+\frac{x^{4}}{64}-\frac{x^{3}}{512}+\frac{x}{4096}-\frac{1}{32768}$$

Solution Steps

Use the distributive property to multiply x-\frac{1}{8} by x^{6}+\frac{1}{64}x^{3}+\frac{1}{4096}.

$$x^{7}+\frac{1}{64}x^{4}+\frac{1}{4096}x-\frac{1}{8}x^{6}-\frac{1}{512}x^{3}-\frac{1}{32768}$$