Solve [14(1/7z^4+1/2)]^2

$$[ 14 ( \frac { 1 } { 7 } z ^ { 4 } + \frac { 1 } { 2 } ) ] ^ { 2 }$$

Evaluate

$$\left(2z^{4}+7\right)^{2}$$

Solution Steps

Use the distributive property to multiply 14 by \frac{1}{7}z^{4}+\frac{1}{2}.

$$\left(2z^{4}+7\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2z^{4}+7\right)^{2}.

$$4\left(z^{4}\right)^{2}+28z^{4}+49$$

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

$$4z^{8}+28z^{4}+49$$

Expand

$$4z^{8}+28z^{4}+49$$

Solution Steps

Use the distributive property to multiply 14 by \frac{1}{7}z^{4}+\frac{1}{2}.

$$\left(2z^{4}+7\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2z^{4}+7\right)^{2}.

$$4\left(z^{4}\right)^{2}+28z^{4}+49$$

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

$$4z^{8}+28z^{4}+49$$