Solve 4:(3y^4-2y^2+8y-16)-(6

$$4 : ( 3 y ^ { 4 } - 2 y ^ { 2 } + 8 y - 16 ) - ( 6$$

Evaluate

$$\frac{2\left(50-24y+6y^{2}-9y^{4}\right)}{3y^{4}-2y^{2}+8y-16}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 6 times \frac{3y^{4}-2y^{2}+8y-16}{3y^{4}-2y^{2}+8y-16}.

$$\frac{4}{3y^{4}-2y^{2}+8y-16}-\frac{6\left(3y^{4}-2y^{2}+8y-16\right)}{3y^{4}-2y^{2}+8y-16}$$

Since \frac{4}{3y^{4}-2y^{2}+8y-16} and \frac{6\left(3y^{4}-2y^{2}+8y-16\right)}{3y^{4}-2y^{2}+8y-16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4-6\left(3y^{4}-2y^{2}+8y-16\right)}{3y^{4}-2y^{2}+8y-16}$$

Do the multiplications in 4-6\left(3y^{4}-2y^{2}+8y-16\right).

$$\frac{4-18y^{4}+12y^{2}-48y+96}{3y^{4}-2y^{2}+8y-16}$$

Combine like terms in 4-18y^{4}+12y^{2}-48y+96.

$$\frac{100-18y^{4}+12y^{2}-48y}{3y^{4}-2y^{2}+8y-16}$$

Factor

$$\frac{2\left(50-24y+6y^{2}-9y^{4}\right)}{3y^{4}-2y^{2}+8y-16}$$