2. Write down the expression that ' \( a \) ' stands for:- \[ 6 x^{3}-4 x^{2} y+8 x y^{2}=a\left(3 x^{2}-2 x y+4 y^{2}\right) \]

To find the expression that \( a \) stands for, we need to simplify the given equation by dividing both sides by the expression inside the parentheses. Given equation: \[ 6x^{3} - 4x^{2}y + 8xy^{2} = a(3x^{2} - 2xy + 4y^{2}) \] To find the value of \( a \), we divide both sides of the equation by the expression inside the parentheses: \[ \frac{6x^{3} - 4x^{2}y + 8xy^{2}}{3x^{2} - 2xy + 4y^{2}} = a \] Now, we simplify the expression on the left side of the equation to find the value of \( a \). Simplify the expression by following steps: - step0: Solution: \(\frac{\left(6x^{3}-4x^{2}y+8xy^{2}\right)}{\left(3x^{2}-2xy+4y^{2}\right)}\) - step1: Remove the parentheses: \(\frac{6x^{3}-4x^{2}y+8xy^{2}}{3x^{2}-2xy+4y^{2}}\) - step2: Factor the expression: \(\frac{2x\left(3x^{2}-2xy+4y^{2}\right)}{3x^{2}-2xy+4y^{2}}\) - step3: Reduce the fraction: \(2x\) The expression that \( a \) stands for is \( 2x \).