Factorise :
(a2+1)b2−b4−a2(a^2 + 1) b^2 - b^4 - a^2(a2+1)b2−b4−a2
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(a2+1)b2−b4−a2=a2b2+b2−b4−a2=(a2b2−a2)+(b2−b4)=a2(b2−1)+b2(1−b2)=a2(b2−1)−b2(b2−1)=(b2−1)(a2−b2)=(b−1)(b+1)(a−b)(a+b)(a^2 + 1) b^2 - b^4 - a^2\\[1em] = a^2b^2 + b^2 - b^4 - a^2\\[1em] = (a^2b^2 - a^2) + (b^2 - b^4)\\[1em] = a^2(b^2 - 1) + b^2(1 - b^2)\\[1em] = a^2(b^2 - 1) - b^2(b^2 - 1)\\[1em] = (b^2 - 1)(a^2 - b^2)\\[1em] = (b - 1)(b + 1)(a - b)(a + b)(a2+1)b2−b4−a2=a2b2+b2−b4−a2=(a2b2−a2)+(b2−b4)=a2(b2−1)+b2(1−b2)=a2(b2−1)−b2(b2−1)=(b2−1)(a2−b2)=(b−1)(b+1)(a−b)(a+b)
Hence, (a2+1)b2−b4−a2=(b−1)(b+1)(a−b)(a+b)(a^2 + 1) b^2 - b^4 - a^2 = (b - 1)(b + 1)(a - b)(a + b)(a2+1)b2−b4−a2=(b−1)(b+1)(a−b)(a+b).
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