Solve {left(1/2y^3-y^1.5right)}^2

$${ \left( \frac{ 1 }{ 2 } { y }^{ 3 } - { y }^{ 1.5 } \right) }^{ 2 }$$

Evaluate

$$\frac{y^{3}\left(y^{1.5}-2\right)^{2}}{4}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\frac{1}{2}y^{3}-y^{1.5}\right)^{2}.

$$\frac{1}{4}\left(y^{3}\right)^{2}-y^{3}y^{1.5}+\left(y^{1.5}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{1}{4}y^{6}-y^{3}y^{1.5}+\left(y^{1.5}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 1.5 to get 4.5.

$$\frac{1}{4}y^{6}-y^{4.5}+\left(y^{1.5}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 1.5 and 2 to get 3.

$$\frac{1}{4}y^{6}-y^{4.5}+y^{3}$$

Expand

$$\frac{y^{6}}{4}-y^{4.5}+y^{3}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\frac{1}{2}y^{3}-y^{1.5}\right)^{2}.

$$\frac{1}{4}\left(y^{3}\right)^{2}-y^{3}y^{1.5}+\left(y^{1.5}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{1}{4}y^{6}-y^{3}y^{1.5}+\left(y^{1.5}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 1.5 to get 4.5.

$$\frac{1}{4}y^{6}-y^{4.5}+\left(y^{1.5}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 1.5 and 2 to get 3.

$$\frac{1}{4}y^{6}-y^{4.5}+y^{3}$$