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\( 1 \leftarrow \quad \) Multiply. Simplify your answer wherever possible. \( 2 x y\left(x^{2}-4 x y+3 y^{2}\right) \)

Ask by Parry Schultz. in the United States
Jan 27,2025

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Answer

The simplified expression is \(2x^{3}y - 8x^{2}y^{2} + 6xy^{3}\).

Solution

Calculate or simplify the expression \( 2*x*y*(x^2-4*x*y+3*y^2) \). Simplify the expression by following steps: - step0: Solution: \(2xy\left(x^{2}-4xy+3y^{2}\right)\) - step1: Rewrite the expression: \(2\left(x^{2}-4xy+3y^{2}\right)xy\) - step2: Multiply the expression: \(2\left(x^{3}y-4x^{2}y^{2}+3y^{3}x\right)\) - step3: Rearrange the terms: \(2x^{3}y-8x^{2}y^{2}+6y^{3}x\) The simplified expression is \(2x^{3}y-8x^{2}y^{2}+6y^{3}x\).

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Mind Expander

To simplify \( 2xy(x^{2} - 4xy + 3y^{2}) \), first, distribute \( 2xy \) into each term inside the parentheses: \[ = 2xy \cdot x^{2} - 2xy \cdot 4xy + 2xy \cdot 3y^{2} \] This gives us: \[ = 2x^{3}y - 8x^{2}y^{2} + 6xy^{3} \] Thus, the fully simplified expression is: \[ 2x^{3}y - 8x^{2}y^{2} + 6xy^{3} \]

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