Solve (36k^2)^2div4(108k^2-12)(3k^2+1)

$$( 36 k ^ { 2 } ) ^ { 2 } \div 4 ( 108 k ^ { 2 } - 12 ) ( 3 k ^ { 2 } + 1 )$$

Evaluate

$$104976k^{8}+23328k^{6}-3888k^{4}$$

Solution Steps

Expand \left(36k^{2}\right)^{2}.

$$\frac{36^{2}\left(k^{2}\right)^{2}}{4}\left(108k^{2}-12\right)\left(3k^{2}+1\right)$$

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

$$\frac{36^{2}k^{4}}{4}\left(108k^{2}-12\right)\left(3k^{2}+1\right)$$

Calculate 36 to the power of 2 and get 1296.

$$\frac{1296k^{4}}{4}\left(108k^{2}-12\right)\left(3k^{2}+1\right)$$

Divide 1296k^{4} by 4 to get 324k^{4}.

$$324k^{4}\left(108k^{2}-12\right)\left(3k^{2}+1\right)$$

Use the distributive property to multiply 324k^{4} by 108k^{2}-12.

$$\left(34992k^{6}-3888k^{4}\right)\left(3k^{2}+1\right)$$

Use the distributive property to multiply 34992k^{6}-3888k^{4} by 3k^{2}+1 and combine like terms.

$$104976k^{8}+23328k^{6}-3888k^{4}$$

Expand

$$104976k^{8}+23328k^{6}-3888k^{4}$$

Solution Steps

Expand \left(36k^{2}\right)^{2}.

$$\frac{36^{2}\left(k^{2}\right)^{2}}{4}\left(108k^{2}-12\right)\left(3k^{2}+1\right)$$

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

$$\frac{36^{2}k^{4}}{4}\left(108k^{2}-12\right)\left(3k^{2}+1\right)$$

Calculate 36 to the power of 2 and get 1296.

$$\frac{1296k^{4}}{4}\left(108k^{2}-12\right)\left(3k^{2}+1\right)$$

Divide 1296k^{4} by 4 to get 324k^{4}.

$$324k^{4}\left(108k^{2}-12\right)\left(3k^{2}+1\right)$$

Use the distributive property to multiply 324k^{4} by 108k^{2}-12.

$$\left(34992k^{6}-3888k^{4}\right)\left(3k^{2}+1\right)$$

Use the distributive property to multiply 34992k^{6}-3888k^{4} by 3k^{2}+1 and combine like terms.

$$104976k^{8}+23328k^{6}-3888k^{4}$$