Solve (2k+4k^{3})(9+24k^{2}+16k^4)-(k^2+k^4)(48k+64k^3)

$$( 2 k + 4 k ^ { 3 } ) ( 9 + 24 k ^ { 2 } + 16 k ^ { 4 } ) - ( k ^ { 2 } + k ^ { 4 } ) ( 48 k + 64 k ^ { 3 } )$$

Evaluate

$$16k^{5}+36k^{3}+18k$$

Solution Steps

Use the distributive property to multiply 2k+4k^{3} by 9+24k^{2}+16k^{4} and combine like terms.

$$18k+84k^{3}+128k^{5}+64k^{7}-\left(k^{2}+k^{4}\right)\left(48k+64k^{3}\right)$$

Use the distributive property to multiply k^{2}+k^{4} by 48k+64k^{3} and combine like terms.

$$18k+84k^{3}+128k^{5}+64k^{7}-\left(48k^{3}+112k^{5}+64k^{7}\right)$$

To find the opposite of 48k^{3}+112k^{5}+64k^{7}, find the opposite of each term.

$$18k+84k^{3}+128k^{5}+64k^{7}-48k^{3}-112k^{5}-64k^{7}$$

Combine 84k^{3} and -48k^{3} to get 36k^{3}.

$$18k+36k^{3}+128k^{5}+64k^{7}-112k^{5}-64k^{7}$$

Combine 128k^{5} and -112k^{5} to get 16k^{5}.

$$18k+36k^{3}+16k^{5}+64k^{7}-64k^{7}$$

Combine 64k^{7} and -64k^{7} to get 0.

$$18k+36k^{3}+16k^{5}$$

Expand

$$16k^{5}+36k^{3}+18k$$

Solution Steps

Use the distributive property to multiply 2k+4k^{3} by 9+24k^{2}+16k^{4} and combine like terms.

$$18k+84k^{3}+128k^{5}+64k^{7}-\left(k^{2}+k^{4}\right)\left(48k+64k^{3}\right)$$

Use the distributive property to multiply k^{2}+k^{4} by 48k+64k^{3} and combine like terms.

$$18k+84k^{3}+128k^{5}+64k^{7}-\left(48k^{3}+112k^{5}+64k^{7}\right)$$

To find the opposite of 48k^{3}+112k^{5}+64k^{7}, find the opposite of each term.

$$18k+84k^{3}+128k^{5}+64k^{7}-48k^{3}-112k^{5}-64k^{7}$$

Combine 84k^{3} and -48k^{3} to get 36k^{3}.

$$18k+36k^{3}+128k^{5}+64k^{7}-112k^{5}-64k^{7}$$

Combine 128k^{5} and -112k^{5} to get 16k^{5}.

$$18k+36k^{3}+16k^{5}+64k^{7}-64k^{7}$$

Combine 64k^{7} and -64k^{7} to get 0.

$$18k+36k^{3}+16k^{5}$$