Solve (1+x+x^2+x^3+x^4+x^5)*(1+x+{x}^2+{x}^3+{x}^4+{x}^5)

$$(1+x+ { x }^{ 2 } + { x }^{ 3 } + { x }^{ 4 } + { x }^{ 5 } ) \times (1+x+ { x }^{ 2 } + { x }^{ 3 } + { x }^{ 4 } + { x }^{ 5 } )$$

Evaluate

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

Solution Steps

Multiply 1+x+x^{2}+x^{3}+x^{4}+x^{5} and 1+x+x^{2}+x^{3}+x^{4}+x^{5} to get \left(1+x+x^{2}+x^{3}+x^{4}+x^{5}\right)^{2}.

$$\left(1+x+x^{2}+x^{3}+x^{4}+x^{5}\right)^{2}$$

Square 1+x+x^{2}+x^{3}+x^{4}+x^{5}.

$$x^{10}+2x^{9}+3x^{8}+4x^{7}+5x^{6}+6x^{5}+5x^{4}+4x^{3}+3x^{2}+2x+1$$

Expand

$$x^{10}+2x^{9}+3x^{8}+4x^{7}+5x^{6}+6x^{5}+5x^{4}+4x^{3}+3x^{2}+2x+1$$

Solution Steps

Multiply 1+x+x^{2}+x^{3}+x^{4}+x^{5} and 1+x+x^{2}+x^{3}+x^{4}+x^{5} to get \left(1+x+x^{2}+x^{3}+x^{4}+x^{5}\right)^{2}.

$$\left(1+x+x^{2}+x^{3}+x^{4}+x^{5}\right)^{2}$$

Square 1+x+x^{2}+x^{3}+x^{4}+x^{5}.

$$x^{10}+2x^{9}+3x^{8}+4x^{7}+5x^{6}+6x^{5}+5x^{4}+4x^{3}+3x^{2}+2x+1$$