Solve (2x^2+x)(x^3+4x)+(x^3+4x)(2x^2+x)

$$( 2 x ^ { 2 } + x ) ( x ^ { 3 } + 4 x ) + ( x ^ { 3 } + 4 x ) ( 2 x ^ { 2 } + x )$$

Evaluate

$$2\left(2x+1\right)x^{2}\left(x^{2}+4\right)$$

Solution Steps

Use the distributive property to multiply 2x^{2}+x by x^{3}+4x.

$$2x^{5}+8x^{3}+x^{4}+4x^{2}+\left(x^{3}+4x\right)\left(2x^{2}+x\right)$$

Use the distributive property to multiply x^{3}+4x by 2x^{2}+x.

$$2x^{5}+8x^{3}+x^{4}+4x^{2}+2x^{5}+x^{4}+8x^{3}+4x^{2}$$

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

$$4x^{5}+8x^{3}+x^{4}+4x^{2}+x^{4}+8x^{3}+4x^{2}$$

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

$$4x^{5}+8x^{3}+2x^{4}+4x^{2}+8x^{3}+4x^{2}$$

Combine 8x^{3} and 8x^{3} to get 16x^{3}.

$$4x^{5}+16x^{3}+2x^{4}+4x^{2}+4x^{2}$$

Combine 4x^{2} and 4x^{2} to get 8x^{2}.

$$4x^{5}+16x^{3}+2x^{4}+8x^{2}$$

Expand

$$4x^{5}+2x^{4}+16x^{3}+8x^{2}$$

Solution Steps

Use the distributive property to multiply 2x^{2}+x by x^{3}+4x.

$$2x^{5}+8x^{3}+x^{4}+4x^{2}+\left(x^{3}+4x\right)\left(2x^{2}+x\right)$$

Use the distributive property to multiply x^{3}+4x by 2x^{2}+x.

$$2x^{5}+8x^{3}+x^{4}+4x^{2}+2x^{5}+x^{4}+8x^{3}+4x^{2}$$

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

$$4x^{5}+8x^{3}+x^{4}+4x^{2}+x^{4}+8x^{3}+4x^{2}$$

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

$$4x^{5}+8x^{3}+2x^{4}+4x^{2}+8x^{3}+4x^{2}$$

Combine 8x^{3} and 8x^{3} to get 16x^{3}.

$$4x^{5}+16x^{3}+2x^{4}+4x^{2}+4x^{2}$$

Combine 4x^{2} and 4x^{2} to get 8x^{2}.

$$4x^{5}+16x^{3}+2x^{4}+8x^{2}$$