Solve a:(2u+3)(u-4)+4u(u-2)

$$a : ( 2 u + 3 ) ( u - 4 ) + 4 u ( u - 2 )$$

Evaluate

$$\frac{8u^{3}-4u^{2}+au-24u-4a}{2u+3}$$

Short Solution Steps

Express \frac{a}{2u+3}\left(u-4\right) as a single fraction.

$$\frac{a\left(u-4\right)}{2u+3}+4u\left(u-2\right)$$

Use the distributive property to multiply 4u by u-2.

$$\frac{a\left(u-4\right)}{2u+3}+4u^{2}-8u$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4u^{2}-8u times \frac{2u+3}{2u+3}.

$$\frac{a\left(u-4\right)}{2u+3}+\frac{\left(4u^{2}-8u\right)\left(2u+3\right)}{2u+3}$$

Since \frac{a\left(u-4\right)}{2u+3} and \frac{\left(4u^{2}-8u\right)\left(2u+3\right)}{2u+3} have the same denominator, add them by adding their numerators.

$$\frac{a\left(u-4\right)+\left(4u^{2}-8u\right)\left(2u+3\right)}{2u+3}$$

Do the multiplications in a\left(u-4\right)+\left(4u^{2}-8u\right)\left(2u+3\right).

$$\frac{au-4a+8u^{3}+12u^{2}-16u^{2}-24u}{2u+3}$$

Combine like terms in au-4a+8u^{3}+12u^{2}-16u^{2}-24u.

$$\frac{-4u^{2}+au+8u^{3}-4a-24u}{2u+3}$$

Expand

$$\frac{8u^{3}-4u^{2}+au-24u-4a}{2u+3}$$

Short Solution Steps

Express \frac{a}{2u+3}\left(u-4\right) as a single fraction.

$$\frac{a\left(u-4\right)}{2u+3}+4u\left(u-2\right)$$

Use the distributive property to multiply 4u by u-2.

$$\frac{a\left(u-4\right)}{2u+3}+4u^{2}-8u$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4u^{2}-8u times \frac{2u+3}{2u+3}.

$$\frac{a\left(u-4\right)}{2u+3}+\frac{\left(4u^{2}-8u\right)\left(2u+3\right)}{2u+3}$$

Since \frac{a\left(u-4\right)}{2u+3} and \frac{\left(4u^{2}-8u\right)\left(2u+3\right)}{2u+3} have the same denominator, add them by adding their numerators.

$$\frac{a\left(u-4\right)+\left(4u^{2}-8u\right)\left(2u+3\right)}{2u+3}$$

Do the multiplications in a\left(u-4\right)+\left(4u^{2}-8u\right)\left(2u+3\right).

$$\frac{au-4a+8u^{3}+12u^{2}-16u^{2}-24u}{2u+3}$$

Combine like terms in au-4a+8u^{3}+12u^{2}-16u^{2}-24u.

$$\frac{-4u^{2}+au+8u^{3}-4a-24u}{2u+3}$$