2. (a) \( 3\left(2 x^{2}\right) \) \( \begin{array}{llll}\text { (b) }(5)\left(2 y^{2}\right) & \text { (c) } 3\left(5 r^{2}\right) & \text { (e) } 3\left(2 b^{2}\right) & \text { (h) }(-2)(-5 y) \\ \text { 3. (a) }(2 x)(4 x) & \text { (d) }(7)\left(4 a^{2}\right) & \text { (f) } 5\left(-2 x^{2}\right) & \text { (g) }-11\left(3 p^{2}\right)\end{array} \)

Sure, let's simplify each of the given algebraic expressions step by step. --- ### **Problem 2** **(a) \( 3\left(2x^{2}\right) \)** Multiply the constants: \[ 3 \times 2x^{2} = 6x^{2} \] --- **(b) \( 5\left(2y^{2}\right) \)** Multiply the constants: \[ 5 \times 2y^{2} = 10y^{2} \] --- **(c) \( 3\left(5r^{2}\right) \)** Multiply the constants: \[ 3 \times 5r^{2} = 15r^{2} \] --- **(e) \( 3\left(2b^{2}\right) \)** Multiply the constants: \[ 3 \times 2b^{2} = 6b^{2} \] --- **(h) \( (-2)(-5y) \)** Multiply the constants, keeping in mind that a negative times a negative is positive: \[ -2 \times -5y = 10y \] --- ### **Problem 3** **(a) \( (2x)(4x) \)** Multiply the constants and add the exponents of like variables: \[ 2x \times 4x = 8x^{2} \] --- **(d) \( 7\left(4a^{2}\right) \)** Multiply the constants: \[ 7 \times 4a^{2} = 28a^{2} \] --- **(f) \( 5\left(-2x^{2}\right) \)** Multiply the constants: \[ 5 \times -2x^{2} = -10x^{2} \] --- **(g) \( -11\left(3p^{2}\right) \)** Multiply the constants: \[ -11 \times 3p^{2} = -33p^{2} \] --- ### **Summary of Simplified Expressions** - **Problem 2** - (a) \( 6x^{2} \) - (b) \( 10y^{2} \) - (c) \( 15r^{2} \) - (e) \( 6b^{2} \) - (h) \( 10y \) - **Problem 3** - (a) \( 8x^{2} \) - (d) \( 28a^{2} \) - (f) \( -10x^{2} \) - (g) \( -33p^{2} \) If you have any further questions or need more explanations on these problems, feel free to ask!