Solve T(x)=(x^2+1)^2(2x+1)

$$T ( x ) = ( x ^ { 2 } + 1 ) ^ { 2 } ( 2 x + 1 )$$

Evaluate

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

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x^{2}+1\right)^{2}.

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

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

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

Use the distributive property to multiply x^{4}+2x^{2}+1 by 2x+1.

$$2x^{5}+x^{4}+4x^{3}+2x^{2}+2x+1$$

Expand

$$2x^{5}+x^{4}+4x^{3}+2x^{2}+2x+1$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x^{2}+1\right)^{2}.

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

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

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

Use the distributive property to multiply x^{4}+2x^{2}+1 by 2x+1.

$$2x^{5}+x^{4}+4x^{3}+2x^{2}+2x+1$$