Solve (h*2h^3-h^3)^2

$$( h \cdot 2 h ^ { 3 } - h ^ { 3 } ) ^ { 2 }$$

Evaluate

$$\left(2h-1\right)^{2}h^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\left(h^{4}\times 2-h^{3}\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(h^{4}\times 2-h^{3}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$4h^{8}-4h^{4}h^{3}+\left(h^{3}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$4h^{8}-4h^{7}+\left(h^{3}\right)^{2}$$

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

$$4h^{8}-4h^{7}+h^{6}$$

Expand

$$4h^{8}-4h^{7}+h^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\left(h^{4}\times 2-h^{3}\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(h^{4}\times 2-h^{3}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$4h^{8}-4h^{4}h^{3}+\left(h^{3}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$4h^{8}-4h^{7}+\left(h^{3}\right)^{2}$$

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

$$4h^{8}-4h^{7}+h^{6}$$