Rewrite (4x^3+x)√(4x^2+1)

asked by guest
on Feb 02, 2025 at 10:22 am



You asked:

Evaluate the expression: (4x3+x)⋅4x2+1\left(4 {x}^{3} + x\right) \cdot \sqrt{4 {x}^{2} + 1}

MathBot Answer:

Evaluated



(4x3+x)⋅4x2+1=4x2+1⋅(4x3+x)\displaystyle \left(4 {x}^{3} + x\right) \cdot \sqrt{4 {x}^{2} + 1} = \sqrt{4 x^{2} + 1} \cdot \left(4 x^{3} + x\right)

Expanded

(4x3+x)⋅4x2+1=4x34x2+1+x4x2+1\left(4 {x}^{3} + x\right) \cdot \sqrt{4 {x}^{2} + 1} = 4 x^{3} \sqrt{4 x^{2} + 1} + x \sqrt{4 x^{2} + 1}

Factored

(4x3+x)⋅4x2+1=x(4x2+1)32\left(4 {x}^{3} + x\right) \cdot \sqrt{4 {x}^{2} + 1} = x \left(4 x^{2} + 1\right)^{\frac{3}{2}}

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