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

Question

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

UpStudy AI · Accepted Answer

Sure, let's simplify each of the given algebraic expressions step by step.

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### **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:

$$
3 \times 2b^{2} = 6b^{2}
$$

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**(h) $$ (-2)(-5y) $$**

Multiply the constants, keeping in mind that a negative times a negative is positive:

$$
-2 \times -5y = 10y
$$

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### **Problem 3**

**(a) $$ (2x)(4x) $$**

Multiply the constants and add the exponents of like variables:

$$
2x \times 4x = 8x^{2}
$$

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**(d) $$ 7\left(4a^{2}\right) $$**

Multiply the constants:

$$
7 \times 4a^{2} = 28a^{2}
$$

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**(f) $$ 5\left(-2x^{2}\right) $$**

Multiply the constants:

$$
5 \times -2x^{2} = -10x^{2}
$$

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**(g) $$ -11\left(3p^{2}\right) $$**

Multiply the constants:

$$
-11 \times 3p^{2} = -33p^{2}
$$

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### **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!
Here are the 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) $$ -33p^{2} $$

(a)

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