Solve (2x^3-3/4x^2+1/2x-1/8)*(x^2-4/3x+4)

$$(2 { x }^{ 3 } - \frac{ 3 }{ 4 } { x }^{ 2 } + \frac{ 1 }{ 2 } x- \frac{ 1 }{ 8 } ) \times ( { x }^{ 2 } - \frac{ 4 }{ 3 } x+4)$$

Evaluate

$$2x^{5}-\frac{41x^{4}}{12}+\frac{19x^{3}}{2}-\frac{91x^{2}}{24}+\frac{13x}{6}-\frac{1}{2}$$

Solution Steps

Use the distributive property to multiply 2x^{3}-\frac{3}{4}x^{2}+\frac{1}{2}x-\frac{1}{8} by x^{2}-\frac{4}{3}x+4 and combine like terms.

$$2x^{5}-\frac{41}{12}x^{4}+\frac{19}{2}x^{3}-\frac{91}{24}x^{2}+\frac{13}{6}x-\frac{1}{2}$$

Expand

$$2x^{5}-\frac{41x^{4}}{12}+\frac{19x^{3}}{2}-\frac{91x^{2}}{24}+\frac{13x}{6}-\frac{1}{2}$$

Solution Steps

Use the distributive property to multiply 2x^{3}-\frac{3}{4}x^{2}+\frac{1}{2}x-\frac{1}{8} by x^{2}-\frac{4}{3}x+4 and combine like terms.

$$2x^{5}-\frac{41}{12}x^{4}+\frac{19}{2}x^{3}-\frac{91}{24}x^{2}+\frac{13}{6}x-\frac{1}{2}$$