Solve (4x^{2}+16x^{2})^2+(4x^2+x^2)^2

$$( 4 x ^ { 2 } + 16 x ^ { 2 } ) ^ { 2 } + ( 4 x ^ { 2 } + x ^ { 2 } ) ^ { 2 }$$

Evaluate

$$425x^{4}$$

Solution Steps

Combine 4x^{2} and 16x^{2} to get 20x^{2}.

$$\left(20x^{2}\right)^{2}+\left(4x^{2}+x^{2}\right)^{2}$$

Expand \left(20x^{2}\right)^{2}.

$$20^{2}\left(x^{2}\right)^{2}+\left(4x^{2}+x^{2}\right)^{2}$$

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

$$20^{2}x^{4}+\left(4x^{2}+x^{2}\right)^{2}$$

Calculate 20 to the power of 2 and get 400.

$$400x^{4}+\left(4x^{2}+x^{2}\right)^{2}$$

Combine 4x^{2} and x^{2} to get 5x^{2}.

$$400x^{4}+\left(5x^{2}\right)^{2}$$

Expand \left(5x^{2}\right)^{2}.

$$400x^{4}+5^{2}\left(x^{2}\right)^{2}$$

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

$$400x^{4}+5^{2}x^{4}$$

Calculate 5 to the power of 2 and get 25.

$$400x^{4}+25x^{4}$$

Combine 400x^{4} and 25x^{4} to get 425x^{4}.

$$425x^{4}$$

Expand

$$425x^{4}$$

Solution Steps

Combine 4x^{2} and 16x^{2} to get 20x^{2}.

$$\left(20x^{2}\right)^{2}+\left(4x^{2}+x^{2}\right)^{2}$$

Expand \left(20x^{2}\right)^{2}.

$$20^{2}\left(x^{2}\right)^{2}+\left(4x^{2}+x^{2}\right)^{2}$$

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

$$20^{2}x^{4}+\left(4x^{2}+x^{2}\right)^{2}$$

Calculate 20 to the power of 2 and get 400.

$$400x^{4}+\left(4x^{2}+x^{2}\right)^{2}$$

Combine 4x^{2} and x^{2} to get 5x^{2}.

$$400x^{4}+\left(5x^{2}\right)^{2}$$

Expand \left(5x^{2}\right)^{2}.

$$400x^{4}+5^{2}\left(x^{2}\right)^{2}$$

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

$$400x^{4}+5^{2}x^{4}$$

Calculate 5 to the power of 2 and get 25.

$$400x^{4}+25x^{4}$$

Combine 400x^{4} and 25x^{4} to get 425x^{4}.

$$425x^{4}$$