36m^6+12m^4+m^2 how so u solve this

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Mathematics

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31 December, 07:09

36m^6+12m^4+m^2 how so u solve this

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Josue Tyler · Answer 1

1. m2 (36 m4 + 12 m2 + 1) 2. Rewrite m4 m4 as (m2) 2 (m2) 2. 3. m2 (36 (m2) 2 + 12 m2 + 1) 4. Let u = m2 u = m2. Substitute uu for all occurrences of m2 m2. = m2 (36u2+12u+1)

5. Rewrite 36 u2 36 u2 as (6u) 2 (6u) 2. 5. m2 ((6u) 2 + 12u+1) 6. Rewrite 11 as 12 7. m2 ((6u) 2 + 12u + 12) 8. Check the middle term by multiplying 2ab and compare this result with the middle term in the original expression. 9. 2ab=2⋅ (6u) ⋅1 2ab=2⋅ (6u) ⋅1 10. Simplify. 2ab=12u

11. Factor using the perfect square trinomial rule a2 + 2ab + b2 = (a+b) 2 a2 + 2ab + b2 = (a+b) 2, where a=6u a=6u and b=1 b=1. 12. m2 (6u+1) 2 m2 (6u+1) 2 13. Replace all occurrences of uu with m2 m2. m^2 (6m^2+1) ^2