Solve left(2x^2-3x+4right)left(6x^2+10x/3-22right)

$$\left( 2 { x }^{ 2 } -3x+4 \right) \left( 6 { x }^{ 2 } +10 \frac{ x }{ 3 } -22 \right)$$

Evaluate

$$12x^{4}-\frac{34x^{3}}{3}-30x^{2}+\frac{238x}{3}-88$$

Short Solution Steps

Express 10\times \frac{x}{3} as a single fraction.

$$\left(2x^{2}-3x+4\right)\left(6x^{2}+\frac{10x}{3}-22\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6x^{2}-22 times \frac{3}{3}.

$$\left(2x^{2}-3x+4\right)\left(\frac{3\left(6x^{2}-22\right)}{3}+\frac{10x}{3}\right)$$

Since \frac{3\left(6x^{2}-22\right)}{3} and \frac{10x}{3} have the same denominator, add them by adding their numerators.

$$\left(2x^{2}-3x+4\right)\times \frac{3\left(6x^{2}-22\right)+10x}{3}$$

Do the multiplications in 3\left(6x^{2}-22\right)+10x.

$$\left(2x^{2}-3x+4\right)\times \frac{18x^{2}-66+10x}{3}$$

Express \left(2x^{2}-3x+4\right)\times \frac{18x^{2}-66+10x}{3} as a single fraction.

$$\frac{\left(2x^{2}-3x+4\right)\left(18x^{2}-66+10x\right)}{3}$$

Use the distributive property to multiply 2x^{2}-3x+4 by 18x^{2}-66+10x and combine like terms.

$$\frac{36x^{4}-90x^{2}-34x^{3}+238x-264}{3}$$

Expand

$$12x^{4}-\frac{34x^{3}}{3}-30x^{2}+\frac{238x}{3}-88$$

Short Solution Steps

Express 10\times \frac{x}{3} as a single fraction.

$$\left(2x^{2}-3x+4\right)\left(6x^{2}+\frac{10x}{3}-22\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6x^{2}-22 times \frac{3}{3}.

$$\left(2x^{2}-3x+4\right)\left(\frac{3\left(6x^{2}-22\right)}{3}+\frac{10x}{3}\right)$$

Since \frac{3\left(6x^{2}-22\right)}{3} and \frac{10x}{3} have the same denominator, add them by adding their numerators.

$$\left(2x^{2}-3x+4\right)\times \frac{3\left(6x^{2}-22\right)+10x}{3}$$

Do the multiplications in 3\left(6x^{2}-22\right)+10x.

$$\left(2x^{2}-3x+4\right)\times \frac{18x^{2}-66+10x}{3}$$

Express \left(2x^{2}-3x+4\right)\times \frac{18x^{2}-66+10x}{3} as a single fraction.

$$\frac{\left(2x^{2}-3x+4\right)\left(18x^{2}-66+10x\right)}{3}$$

Use the distributive property to multiply 2x^{2}-3x+4 by 18x^{2}-66+10x and combine like terms.

$$\frac{36x^{4}-90x^{2}-34x^{3}+238x-264}{3}$$