Solve (2/5x^4-3)^2

$$( \frac { 2 } { 5 } x ^ { 4 } - 3 ) ^ { 2 }$$

Evaluate

$$\frac{\left(2x^{4}-15\right)^{2}}{25}$$

Solution Steps

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

$$\frac{4}{25}\left(x^{4}\right)^{2}-\frac{12}{5}x^{4}+9$$

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

$$\frac{4}{25}x^{8}-\frac{12}{5}x^{4}+9$$

Expand

$$\frac{4x^{8}}{25}-\frac{12x^{4}}{5}+9$$

Solution Steps

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

$$\frac{4}{25}\left(x^{4}\right)^{2}-\frac{12}{5}x^{4}+9$$

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

$$\frac{4}{25}x^{8}-\frac{12}{5}x^{4}+9$$