Solve 16+x-10/2(8)+5x^2-90x+400/8+x^3-24x^2+188x-480/12

$$16 + \frac { x - 10 } { 2 } ( 8 ) + \frac { 5 x ^ { 2 } - 90 x + 400 } { 8 } + \frac { x ^ { 3 } - 24 x ^ { 2 } + 188 x - 480 } { 12 }$$

Evaluate

$$\frac{x^{3}}{12}-\frac{11x^{2}}{8}+\frac{101x}{12}-14$$

Short Solution Steps

Cancel out 2, the greatest common factor in 8 and 2.

$$16+4\left(x-10\right)+\frac{5x^{2}-90x+400}{8}+\frac{x^{3}-24x^{2}+188x-480}{12}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 16 times \frac{8}{8}.

$$\frac{16\times 8}{8}+4\left(x-10\right)+\frac{5x^{2}-90x+400}{8}+\frac{x^{3}-24x^{2}+188x-480}{12}$$

Since \frac{16\times 8}{8} and \frac{5x^{2}-90x+400}{8} have the same denominator, add them by adding their numerators.

$$\frac{16\times 8+5x^{2}-90x+400}{8}+4\left(x-10\right)+\frac{x^{3}-24x^{2}+188x-480}{12}$$

Do the multiplications in 16\times 8+5x^{2}-90x+400.

$$\frac{128+5x^{2}-90x+400}{8}+4\left(x-10\right)+\frac{x^{3}-24x^{2}+188x-480}{12}$$

Combine like terms in 128+5x^{2}-90x+400.

$$\frac{528+5x^{2}-90x}{8}+4\left(x-10\right)+\frac{x^{3}-24x^{2}+188x-480}{12}$$

Use the distributive property to multiply 4 by x-10.

$$16+4x-40+\frac{5x^{2}-90x+400}{8}+\frac{x^{3}-24x^{2}+188x-480}{12}$$

Subtract 40 from 16 to get -24.

$$-24+4x+\frac{5x^{2}-90x+400}{8}+\frac{x^{3}-24x^{2}+188x-480}{12}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -24+4x times \frac{8}{8}.

$$\frac{8\left(-24+4x\right)}{8}+\frac{5x^{2}-90x+400}{8}+\frac{x^{3}-24x^{2}+188x-480}{12}$$

Since \frac{8\left(-24+4x\right)}{8} and \frac{5x^{2}-90x+400}{8} have the same denominator, add them by adding their numerators.

$$\frac{8\left(-24+4x\right)+5x^{2}-90x+400}{8}+\frac{x^{3}-24x^{2}+188x-480}{12}$$

Do the multiplications in 8\left(-24+4x\right)+5x^{2}-90x+400.

$$\frac{-192+32x+5x^{2}-90x+400}{8}+\frac{x^{3}-24x^{2}+188x-480}{12}$$

Combine like terms in -192+32x+5x^{2}-90x+400.

$$\frac{208-58x+5x^{2}}{8}+\frac{x^{3}-24x^{2}+188x-480}{12}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8 and 12 is 24. Multiply \frac{208-58x+5x^{2}}{8} times \frac{3}{3}. Multiply \frac{x^{3}-24x^{2}+188x-480}{12} times \frac{2}{2}.

$$\frac{3\left(208-58x+5x^{2}\right)}{24}+\frac{2\left(x^{3}-24x^{2}+188x-480\right)}{24}$$

Since \frac{3\left(208-58x+5x^{2}\right)}{24} and \frac{2\left(x^{3}-24x^{2}+188x-480\right)}{24} have the same denominator, add them by adding their numerators.

$$\frac{3\left(208-58x+5x^{2}\right)+2\left(x^{3}-24x^{2}+188x-480\right)}{24}$$

Do the multiplications in 3\left(208-58x+5x^{2}\right)+2\left(x^{3}-24x^{2}+188x-480\right).

$$\frac{624-174x+15x^{2}+2x^{3}-48x^{2}+376x-960}{24}$$

Combine like terms in 624-174x+15x^{2}+2x^{3}-48x^{2}+376x-960.

$$\frac{-336+202x-33x^{2}+2x^{3}}{24}$$

Expand

$$\frac{x^{3}}{12}-\frac{11x^{2}}{8}+\frac{101x}{12}-14$$

Short Solution Steps

Cancel out 2, the greatest common factor in 8 and 2.

$$16+4\left(x-10\right)+\frac{5x^{2}-90x+400}{8}+\frac{x^{3}-24x^{2}+188x-480}{12}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 16 times \frac{8}{8}.

$$\frac{16\times 8}{8}+4\left(x-10\right)+\frac{5x^{2}-90x+400}{8}+\frac{x^{3}-24x^{2}+188x-480}{12}$$

Since \frac{16\times 8}{8} and \frac{5x^{2}-90x+400}{8} have the same denominator, add them by adding their numerators.

$$\frac{16\times 8+5x^{2}-90x+400}{8}+4\left(x-10\right)+\frac{x^{3}-24x^{2}+188x-480}{12}$$

Do the multiplications in 16\times 8+5x^{2}-90x+400.

$$\frac{128+5x^{2}-90x+400}{8}+4\left(x-10\right)+\frac{x^{3}-24x^{2}+188x-480}{12}$$

Combine like terms in 128+5x^{2}-90x+400.

$$\frac{528+5x^{2}-90x}{8}+4\left(x-10\right)+\frac{x^{3}-24x^{2}+188x-480}{12}$$

Use the distributive property to multiply 4 by x-10.

$$16+4x-40+\frac{5x^{2}-90x+400}{8}+\frac{x^{3}-24x^{2}+188x-480}{12}$$

Subtract 40 from 16 to get -24.

$$-24+4x+\frac{5x^{2}-90x+400}{8}+\frac{x^{3}-24x^{2}+188x-480}{12}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -24+4x times \frac{8}{8}.

$$\frac{8\left(-24+4x\right)}{8}+\frac{5x^{2}-90x+400}{8}+\frac{x^{3}-24x^{2}+188x-480}{12}$$

Since \frac{8\left(-24+4x\right)}{8} and \frac{5x^{2}-90x+400}{8} have the same denominator, add them by adding their numerators.

$$\frac{8\left(-24+4x\right)+5x^{2}-90x+400}{8}+\frac{x^{3}-24x^{2}+188x-480}{12}$$

Do the multiplications in 8\left(-24+4x\right)+5x^{2}-90x+400.

$$\frac{-192+32x+5x^{2}-90x+400}{8}+\frac{x^{3}-24x^{2}+188x-480}{12}$$

Combine like terms in -192+32x+5x^{2}-90x+400.

$$\frac{208-58x+5x^{2}}{8}+\frac{x^{3}-24x^{2}+188x-480}{12}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8 and 12 is 24. Multiply \frac{208-58x+5x^{2}}{8} times \frac{3}{3}. Multiply \frac{x^{3}-24x^{2}+188x-480}{12} times \frac{2}{2}.

$$\frac{3\left(208-58x+5x^{2}\right)}{24}+\frac{2\left(x^{3}-24x^{2}+188x-480\right)}{24}$$

Since \frac{3\left(208-58x+5x^{2}\right)}{24} and \frac{2\left(x^{3}-24x^{2}+188x-480\right)}{24} have the same denominator, add them by adding their numerators.

$$\frac{3\left(208-58x+5x^{2}\right)+2\left(x^{3}-24x^{2}+188x-480\right)}{24}$$

Do the multiplications in 3\left(208-58x+5x^{2}\right)+2\left(x^{3}-24x^{2}+188x-480\right).

$$\frac{624-174x+15x^{2}+2x^{3}-48x^{2}+376x-960}{24}$$

Combine like terms in 624-174x+15x^{2}+2x^{3}-48x^{2}+376x-960.

$$\frac{-336+202x-33x^{2}+2x^{3}}{24}$$