Solve (4y^3-0,5y^2)^2

$$( 4 y ^ { 3 } - 0,5 y ^ { 2 } ) ^ { 2 }$$

Evaluate

$$\left(4y-0,5\right)^{2}y^{4}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(4y^{3}-0,5y^{2}\right)^{2}.

$$16\left(y^{3}\right)^{2}-4y^{3}y^{2}+0,25\left(y^{2}\right)^{2}$$

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

$$16y^{6}-4y^{3}y^{2}+0,25\left(y^{2}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$16y^{6}-4y^{5}+0,25\left(y^{2}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$16y^{6}-4y^{5}+0,25y^{4}$$

Expand

$$16y^{6}-4y^{5}+\frac{y^{4}}{4}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(4y^{3}-0,5y^{2}\right)^{2}.

$$16\left(y^{3}\right)^{2}-4y^{3}y^{2}+0,25\left(y^{2}\right)^{2}$$

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

$$16y^{6}-4y^{3}y^{2}+0,25\left(y^{2}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$16y^{6}-4y^{5}+0,25\left(y^{2}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$16y^{6}-4y^{5}+0,25y^{4}$$