Final Answer
$\left(a-1\right)^{2}\left(\frac{3}{4}+\left(a+\frac{1}{2}\right)^2\right)^{2}$
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Step-by-step Solution
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1
The trinomial $1-2a^3+a^6$ is a perfect square trinomial, because it's discriminant is equal to zero
$\Delta=b^2-4ac=-2^2-4\left(1\right)\left(1\right) = 0$
Learn how to solve polynomial factorization problems step by step online.
$\Delta=b^2-4ac=-2^2-4\left(1\right)\left(1\right) = 0$
Learn how to solve polynomial factorization problems step by step online. Factor the expression 1-2a^3a^6. The trinomial 1-2a^3+a^6 is a perfect square trinomial, because it's discriminant is equal to zero. Using the perfect square trinomial formula. Factoring the perfect square trinomial. Factor the sum or difference of cubes using the formula: a^3\pm b^3 = (a\pm b)(a^2\mp ab+b^2).
Final Answer
$\left(a-1\right)^{2}\left(\frac{3}{4}+\left(a+\frac{1}{2}\right)^2\right)^{2}$