Solve 15(y+3)(y^2-16)div5(y^2-y-12)

$$15 ( y + 3 ) ( y ^ { 2 } - 16 ) \div 5 ( y ^ { 2 } - y - 12 )$$

Evaluate

$$3\left(y+4\right)\left(\left(y-4\right)\left(y+3\right)\right)^{2}$$

Solution Steps

Use the distributive property to multiply 15 by y+3.

$$\frac{\left(15y+45\right)\left(y^{2}-16\right)}{5}\left(y^{2}-y-12\right)$$

Use the distributive property to multiply 15y+45 by y^{2}-16.

$$\frac{15y^{3}-240y+45y^{2}-720}{5}\left(y^{2}-y-12\right)$$

Express \frac{15y^{3}-240y+45y^{2}-720}{5}\left(y^{2}-y-12\right) as a single fraction.

$$\frac{\left(15y^{3}-240y+45y^{2}-720\right)\left(y^{2}-y-12\right)}{5}$$

Use the distributive property to multiply 15y^{3}-240y+45y^{2}-720 by y^{2}-y-12 and combine like terms.

$$\frac{15y^{5}+30y^{4}-465y^{3}-1020y^{2}+3600y+8640}{5}$$

Expand

$$3y^{5}+6y^{4}-93y^{3}-204y^{2}+720y+1728$$

Solution Steps

Use the distributive property to multiply 15 by y+3.

$$\frac{\left(15y+45\right)\left(y^{2}-16\right)}{5}\left(y^{2}-y-12\right)$$

Use the distributive property to multiply 15y+45 by y^{2}-16.

$$\frac{15y^{3}-240y+45y^{2}-720}{5}\left(y^{2}-y-12\right)$$

Express \frac{15y^{3}-240y+45y^{2}-720}{5}\left(y^{2}-y-12\right) as a single fraction.

$$\frac{\left(15y^{3}-240y+45y^{2}-720\right)\left(y^{2}-y-12\right)}{5}$$

Use the distributive property to multiply 15y^{3}-240y+45y^{2}-720 by y^{2}-y-12 and combine like terms.

$$\frac{15y^{5}+30y^{4}-465y^{3}-1020y^{2}+3600y+8640}{5}$$