Solve (y^4/4-3y+9)(12y^5+8y-4)

$$( \frac { y ^ { 4 } } { 4 } - 3 y + 9 ) ( 12 y ^ { 5 } + 8 y - 4 )$$

Evaluate

$$\left(y^{4}-12y+36\right)\left(3y^{5}+2y-1\right)$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply -3y+9 times \frac{4}{4}.

$$\left(\frac{y^{4}}{4}+\frac{4\left(-3y+9\right)}{4}\right)\left(12y^{5}+8y-4\right)$$

Since \frac{y^{4}}{4} and \frac{4\left(-3y+9\right)}{4} have the same denominator, add them by adding their numerators.

$$\frac{y^{4}+4\left(-3y+9\right)}{4}\left(12y^{5}+8y-4\right)$$

Do the multiplications in y^{4}+4\left(-3y+9\right).

$$\frac{y^{4}-12y+36}{4}\left(12y^{5}+8y-4\right)$$

Express \frac{y^{4}-12y+36}{4}\left(12y^{5}+8y-4\right) as a single fraction.

$$\frac{\left(y^{4}-12y+36\right)\left(12y^{5}+8y-4\right)}{4}$$

Use the distributive property to multiply y^{4}-12y+36 by 12y^{5}+8y-4 and combine like terms.

$$\frac{12y^{9}+440y^{5}-4y^{4}-144y^{6}-96y^{2}+336y-144}{4}$$

Divide each term of 12y^{9}+440y^{5}-4y^{4}-144y^{6}-96y^{2}+336y-144 by 4 to get -36-36y^{6}+3y^{9}+84y-y^{4}+110y^{5}-24y^{2}.

$$-36-36y^{6}+3y^{9}+84y-y^{4}+110y^{5}-24y^{2}$$

Expand

$$3y^{9}-36y^{6}+110y^{5}-y^{4}-24y^{2}+84y-36$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply -3y+9 times \frac{4}{4}.

$$\left(\frac{y^{4}}{4}+\frac{4\left(-3y+9\right)}{4}\right)\left(12y^{5}+8y-4\right)$$

Since \frac{y^{4}}{4} and \frac{4\left(-3y+9\right)}{4} have the same denominator, add them by adding their numerators.

$$\frac{y^{4}+4\left(-3y+9\right)}{4}\left(12y^{5}+8y-4\right)$$

Do the multiplications in y^{4}+4\left(-3y+9\right).

$$\frac{y^{4}-12y+36}{4}\left(12y^{5}+8y-4\right)$$

Express \frac{y^{4}-12y+36}{4}\left(12y^{5}+8y-4\right) as a single fraction.

$$\frac{\left(y^{4}-12y+36\right)\left(12y^{5}+8y-4\right)}{4}$$

Use the distributive property to multiply y^{4}-12y+36 by 12y^{5}+8y-4 and combine like terms.

$$\frac{12y^{9}+440y^{5}-4y^{4}-144y^{6}-96y^{2}+336y-144}{4}$$

Divide each term of 12y^{9}+440y^{5}-4y^{4}-144y^{6}-96y^{2}+336y-144 by 4 to get -36-36y^{6}+3y^{9}+84y-y^{4}+110y^{5}-24y^{2}.

$$-36-36y^{6}+3y^{9}+84y-y^{4}+110y^{5}-24y^{2}$$