Question

Factor completely 12t ^8-75t^4

Answer 1

$12t^8-75t^4=3t^4\cdot4t^4-3t^4\cdot25=3t^4(4t^4-25)\\\\=3t^4[(2t^2)^2-5^2]\\\\use\ a^2-b^2=(a-b)(a+b)\\\\=3t^4(2t^2-5)(2t^2+5)=3t^4[(t\sqrt2)^2-(\sqrt5)^2](2t^2+5)\\\\=3t^4(t\sqrt2-\sqrt5)(t\sqrt2+\sqrt5)(2t^2+5)$