Solve (8w^4+w^3)^2=

$$( 8 w ^ { 4 } + w ^ { 3 } ) ^ { 2 } =$$

Evaluate

$$\left(8w+1\right)^{2}w^{6}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(8w^{4}+w^{3}\right)^{2}.

$$64\left(w^{4}\right)^{2}+16w^{4}w^{3}+\left(w^{3}\right)^{2}$$

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

$$64w^{8}+16w^{4}w^{3}+\left(w^{3}\right)^{2}$$

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

$$64w^{8}+16w^{7}+\left(w^{3}\right)^{2}$$

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

$$64w^{8}+16w^{7}+w^{6}$$

Expand

$$64w^{8}+16w^{7}+w^{6}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(8w^{4}+w^{3}\right)^{2}.

$$64\left(w^{4}\right)^{2}+16w^{4}w^{3}+\left(w^{3}\right)^{2}$$

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

$$64w^{8}+16w^{4}w^{3}+\left(w^{3}\right)^{2}$$

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

$$64w^{8}+16w^{7}+\left(w^{3}\right)^{2}$$

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

$$64w^{8}+16w^{7}+w^{6}$$