Solve (3x^2+x/2)(2x^2-4x+10)

$$( 3 x ^ { 2 } + \frac { x } { 2 } ) ( 2 x ^ { 2 } - 4 x + 10 )$$

Evaluate

$$x\left(6x+1\right)\left(x^{2}-2x+5\right)$$

Short Solution Steps

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

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

Since \frac{2\times 3x^{2}}{2} and \frac{x}{2} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 2\times 3x^{2}+x.

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

Express \frac{6x^{2}+x}{2}\left(2x^{2}-4x+10\right) as a single fraction.

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

Use the distributive property to multiply 6x^{2}+x by 2x^{2}-4x+10 and combine like terms.

$$\frac{12x^{4}-22x^{3}+56x^{2}+10x}{2}$$

Divide each term of 12x^{4}-22x^{3}+56x^{2}+10x by 2 to get 5x+28x^{2}-11x^{3}+6x^{4}.

$$5x+28x^{2}-11x^{3}+6x^{4}$$

Expand

$$6x^{4}-11x^{3}+28x^{2}+5x$$

Short Solution Steps

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

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

Since \frac{2\times 3x^{2}}{2} and \frac{x}{2} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 2\times 3x^{2}+x.

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

Express \frac{6x^{2}+x}{2}\left(2x^{2}-4x+10\right) as a single fraction.

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

Use the distributive property to multiply 6x^{2}+x by 2x^{2}-4x+10 and combine like terms.

$$\frac{12x^{4}-22x^{3}+56x^{2}+10x}{2}$$

Divide each term of 12x^{4}-22x^{3}+56x^{2}+10x by 2 to get 5x+28x^{2}-11x^{3}+6x^{4}.

$$5x+28x^{2}-11x^{3}+6x^{4}$$