Solve (-1+10k^3)^2=

$$( - 1 + 10 k ^ { 3 } ) ^ { 2 } =$$

Evaluate

$$\left(10k^{3}-1\right)^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(-1+10k^{3}\right)^{2}.

$$1-20k^{3}+100\left(k^{3}\right)^{2}$$

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

$$1-20k^{3}+100k^{6}$$

Expand

$$100k^{6}-20k^{3}+1$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(-1+10k^{3}\right)^{2}.

$$1-20k^{3}+100\left(k^{3}\right)^{2}$$

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

$$1-20k^{3}+100k^{6}$$