Expand the given mathematical expression: 7. $(2 x+1)\left(x^{2}+3 x-1\right)$

Step 1 ：Given the mathematical expression: \( (2x + 1)(x^{2} + 3x - 1) \)

Step 2 ：To expand the given mathematical expression, we need to apply the distributive property of multiplication over addition. This means we multiply each term inside the first bracket by each term inside the second bracket.

Step 3 ：First, multiply \(2x\) by each term in the second bracket: \(2x * x^{2} = 2x^{3}\), \(2x * 3x = 6x^{2}\), \(2x * -1 = -2x\)

Step 4 ：Next, multiply \(1\) by each term in the second bracket: \(1 * x^{2} = x^{2}\), \(1 * 3x = 3x\), \(1 * -1 = -1\)

Step 5 ：Combine like terms: \(2x^{3} + 6x^{2} + x^{2} + 3x - 2x - 1 = 2x^{3} + 7x^{2} + x - 1\)

Step 6 ：Final Answer: The expanded form of the given mathematical expression is \(\boxed{2x^{3} + 7x^{2} + x - 1}\)