Solve [K(K+48)][64-4K]-[16+K][4][K+16]

$$[ K ( K + 48 ) ] [ 64 - 4 K ] - [ 16 + K ] [ 4 ] [ K + 16 ]$$

Evaluate

$$-4K^{3}-132K^{2}+2944K-1024$$

Solution Steps

Multiply 16+K and K+16 to get \left(16+K\right)^{2}.

$$K\left(K+48\right)\left(64-4K\right)-\left(16+K\right)^{2}\times 4$$

Use the distributive property to multiply K by K+48.

$$\left(K^{2}+48K\right)\left(64-4K\right)-\left(16+K\right)^{2}\times 4$$

Apply the distributive property by multiplying each term of K^{2}+48K by each term of 64-4K.

$$64K^{2}-4K^{3}+3072K-192K^{2}-\left(16+K\right)^{2}\times 4$$

Combine 64K^{2} and -192K^{2} to get -128K^{2}.

$$-128K^{2}-4K^{3}+3072K-\left(16+K\right)^{2}\times 4$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(16+K\right)^{2}.

$$-128K^{2}-4K^{3}+3072K-\left(256+32K+K^{2}\right)\times 4$$

Use the distributive property to multiply 256+32K+K^{2} by 4.

$$-128K^{2}-4K^{3}+3072K-\left(1024+128K+4K^{2}\right)$$

To find the opposite of 1024+128K+4K^{2}, find the opposite of each term.

$$-128K^{2}-4K^{3}+3072K-1024-128K-4K^{2}$$

Combine 3072K and -128K to get 2944K.

$$-128K^{2}-4K^{3}+2944K-1024-4K^{2}$$

Combine -128K^{2} and -4K^{2} to get -132K^{2}.

$$-132K^{2}-4K^{3}+2944K-1024$$

Expand

$$-4K^{3}-132K^{2}+2944K-1024$$

Solution Steps

Multiply 16+K and K+16 to get \left(16+K\right)^{2}.

$$K\left(K+48\right)\left(64-4K\right)-\left(16+K\right)^{2}\times 4$$

Use the distributive property to multiply K by K+48.

$$\left(K^{2}+48K\right)\left(64-4K\right)-\left(16+K\right)^{2}\times 4$$

Apply the distributive property by multiplying each term of K^{2}+48K by each term of 64-4K.

$$64K^{2}-4K^{3}+3072K-192K^{2}-\left(16+K\right)^{2}\times 4$$

Combine 64K^{2} and -192K^{2} to get -128K^{2}.

$$-128K^{2}-4K^{3}+3072K-\left(16+K\right)^{2}\times 4$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(16+K\right)^{2}.

$$-128K^{2}-4K^{3}+3072K-\left(256+32K+K^{2}\right)\times 4$$

Use the distributive property to multiply 256+32K+K^{2} by 4.

$$-128K^{2}-4K^{3}+3072K-\left(1024+128K+4K^{2}\right)$$

To find the opposite of 1024+128K+4K^{2}, find the opposite of each term.

$$-128K^{2}-4K^{3}+3072K-1024-128K-4K^{2}$$

Combine 3072K and -128K to get 2944K.

$$-128K^{2}-4K^{3}+2944K-1024-4K^{2}$$

Combine -128K^{2} and -4K^{2} to get -132K^{2}.

$$-132K^{2}-4K^{3}+2944K-1024$$