Question

question
express in simplest radical form given ( x > 0 ).
( -4x^2sqrt{63x^2} + x^3sqrt{112} )
answer attempt 1 out of 2
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Explanation:

Step1: Simplify $\sqrt{63x^2}$

Factor radicand: $\sqrt{63x^2}=\sqrt{9x^2 \cdot 7}=3x\sqrt{7}$ (since $x>0$)

Step2: Simplify $\sqrt{112}$

Factor radicand: $\sqrt{112}=\sqrt{16 \cdot 7}=4\sqrt{7}$

Step3: Substitute back to original expression

$-4x^2 \cdot 3x\sqrt{7} + x^3 \cdot 4\sqrt{7}$

Step4: Calculate each term

$-12x^3\sqrt{7} + 4x^3\sqrt{7}$

Step5: Combine like terms

$(-12+4)x^3\sqrt{7}=-8x^3\sqrt{7}$

Answer:

$-8x^3\sqrt{7}$