Solve 2a(1+x^2)^2-a(1-x^0)(0)^2

$$2 a ( 1 + x ^ { 2 } ) ^ { 2 } - a ( 1 - x ^ { 0 } ) ( 0 ) ^ { 2 }$$

Factor

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

Solution Steps

Factor out common term a by using distributive property.

$$a\left(2\left(1+x^{2}\right)^{2}-\left(1-x^{0}\right)\times 0^{2}\right)$$

Consider 2\left(1+x^{2}\right)^{2}-\left(1-x^{0}\right)\times 0^{2}. Simplify.

$$2x^{4}+4x^{2}+2$$

Factor out 2.

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

Consider x^{4}+2x^{2}+1. Use the perfect square formula, p^{2}+2pq+q^{2}=\left(p+q\right)^{2}, where p=x^{2} and q=1.

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

Rewrite the complete factored expression.

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

Rewrite the complete factored expression. Simplify. Polynomial x^{2}+1 is not factored since it does not have any rational roots.

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

Evaluate

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