Simplify as much as possible. Assume that all variables represent positive real numbers.
\[ 4x\sqrt{32xv^2} + v\sqrt{2x^3} \]
Answer (3)
4 x 32 x v 2 + v 2 x 3 = 4 x 16 ⋅ 2 ⋅ x ⋅ v 2 + v 2 ⋅ x 2 ⋅ x = 4 x ⋅ 4 2 ⋅ x ⋅ v + v 2 ⋅ x x = 16 xv 2 x + xv 2 x = 17 2 x ======================================== D ; x ∈< 0 ; ∞ ) ∧ v ∈ R
4 x 32 x v 2 + v 2 x 3 = 4 x 16.2 . x . v 2 + v 2 . x 2 . x = 4 x . 2 . x . v + v 2 . x x = 16 xv 2 x + xv 2 x = 17 2 x
The expression 4 x 32 x v 2 + v 2 x 3 simplifies to 17 xv 2 x . Each term was simplified separately before combining. The final result is a clean, single term that represents the combination of all components.
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