Expand and simplify: \( \begin{array}{lllll}\text { (1) } \quad \begin{array}{l}\text { in } \\ \text { ( } x+3)\end{array} & \text { (2) } & -3 v\left(3 a^{3}-6 a^{2}+a\right) & \text { (3) } & (x+5)(x+3 \\ \text { (4) }(x-5)(x-2) & \text { (5) } & (x+5)(x-2) & \text { (4) } & (x-5)(x+3 \\ \text { (7) }(3 x-1)(2 x+3) & \text { (8) } & (7 m-2 \pi)(3 m+4 n) & \\ \text { (9) }\left(2 x^{4}-3 y^{2}\right)\left(3 x^{4}+2 y^{2}\right) & \text { (10) }\left(4 x^{4}+3 y^{5}\right)\left(2 x^{4}-4 y^{3}\right)\end{array} \) Exnand and simnlifi-

Simplify the expression by following steps: - step0: Multiply the terms: \(\left(x-5\right)\left(x-2\right)\) - step1: Apply the distributive property: \(x\times x-x\times 2-5x-\left(-5\times 2\right)\) - step2: Multiply the terms: \(x^{2}-2x-5x-\left(-10\right)\) - step3: Remove the parentheses: \(x^{2}-2x-5x+10\) - step4: Subtract the terms: \(x^{2}-7x+10\) Expand the expression \( (3 x-1)(2 x+3) \) Simplify the expression by following steps: - step0: Multiply the terms: \(\left(3x-1\right)\left(2x+3\right)\) - step1: Apply the distributive property: \(3x\times 2x+3x\times 3-2x-3\) - step2: Multiply the terms: \(6x^{2}+9x-2x-3\) - step3: Subtract the terms: \(6x^{2}+7x-3\) Expand the expression \( (x-5)(x+3) \) Simplify the expression by following steps: - step0: Multiply the terms: \(\left(x-5\right)\left(x+3\right)\) - step1: Apply the distributive property: \(x\times x+x\times 3-5x-5\times 3\) - step2: Multiply the terms: \(x^{2}+3x-5x-15\) - step3: Subtract the terms: \(x^{2}-2x-15\) Expand the expression \( -3 v(3 a^{3}-6 a^{2}+a) \) Simplify the expression by following steps: - step0: Simplify: \(-3v\left(3a^{3}-6a^{2}+a\right)\) - step1: Rewrite the expression: \(-3\left(3a^{3}-6a^{2}+a\right)v\) - step2: Multiply the expression: \(-3\left(3a^{3}v-6a^{2}v+av\right)\) - step3: Rearrange the terms: \(-9a^{3}v+18a^{2}v-3av\) Expand the expression \( (x+5)(x-2) \) Simplify the expression by following steps: - step0: Multiply the terms: \(\left(x+5\right)\left(x-2\right)\) - step1: Apply the distributive property: \(x\times x-x\times 2+5x-5\times 2\) - step2: Multiply the terms: \(x^{2}-2x+5x-10\) - step3: Add the terms: \(x^{2}+3x-10\) Expand the expression \( (7 m-2 \pi)(3 m+4 n) \) Simplify the expression by following steps: - step0: Multiply the terms: \(\left(7m-2\pi \right)\left(3m+4n\right)\) - step1: Apply the distributive property: \(7m\times 3m+7m\times 4n-2\pi \times 3m-2\pi \times 4n\) - step2: Multiply the terms: \(21m^{2}+28mn-6\pi m-8\pi n\) Expand the expression \( (2 x^{4}-3 y^{2})(3 x^{4}+2 y^{2}) \) Simplify the expression by following steps: - step0: Multiply the terms: \(\left(2x^{4}-3y^{2}\right)\left(3x^{4}+2y^{2}\right)\) - step1: Apply the distributive property: \(2x^{4}\times 3x^{4}+2x^{4}\times 2y^{2}-3y^{2}\times 3x^{4}-3y^{2}\times 2y^{2}\) - step2: Multiply the terms: \(6x^{8}+4x^{4}y^{2}-9y^{2}x^{4}-6y^{4}\) - step3: Subtract the terms: \(6x^{8}-5x^{4}y^{2}-6y^{4}\) Expand the expression \( (4 x^{4}+3 y^{5})(2 x^{4}-4 y^{3}) \) Simplify the expression by following steps: - step0: Multiply the terms: \(\left(4x^{4}+3y^{5}\right)\left(2x^{4}-4y^{3}\right)\) - step1: Apply the distributive property: \(4x^{4}\times 2x^{4}-4x^{4}\times 4y^{3}+3y^{5}\times 2x^{4}-3y^{5}\times 4y^{3}\) - step2: Multiply the terms: \(8x^{8}-16x^{4}y^{3}+6y^{5}x^{4}-12y^{8}\) Expand the expression \( (x+3) \) Simplify the expression by following steps: - step0: Remove the parentheses: \(\left(x+3\right)\) - step1: Remove the parentheses: \(x+3\) Expand the expression \( (x+5)(x+3) \) Simplify the expression by following steps: - step0: Multiply the terms: \(\left(x+5\right)\left(x+3\right)\) - step1: Apply the distributive property: \(x\times x+x\times 3+5x+5\times 3\) - step2: Multiply the terms: \(x^{2}+3x+5x+15\) - step3: Add the terms: \(x^{2}+8x+15\) Here are the expanded and simplified results for each expression: 1. **Expression:** \( (x+3) \) **Expanded:** \( x + 3 \) 2. **Expression:** \( -3 v(3 a^{3}-6 a^{2}+a) \) **Expanded:** \( -9a^{3}v + 18a^{2}v - 3av \) 3. **Expression:** \( (x+5)(x+3) \) **Expanded:** \( x^{2} + 8x + 15 \) 4. **Expression:** \( (x-5)(x-2) \) **Expanded:** \( x^{2} - 7x + 10 \) 5. **Expression:** \( (x+5)(x-2) \) **Expanded:** \( x^{2} + 3x - 10 \) 6. **Expression:** \( (x-5)(x+3) \) **Expanded:** \( x^{2} - 2x - 15 \) 7. **Expression:** \( (3 x-1)(2 x+3) \) **Expanded:** \( 6x^{2} + 7x - 3 \) 8. **Expression:** \( (7 m-2 \pi)(3 m+4 n) \) **Expanded:** \( 21m^{2} + 28mn - 6\pi m - 8\pi n \) 9. **Expression:** \( (2 x^{4}-3 y^{2})(3 x^{4}+2 y^{2}) \) **Expanded:** \( 6x^{8} - 5x^{4}y^{2} - 6y^{4} \) 10. **Expression:** \( (4 x^{4}+3 y^{5})(2 x^{4}-4 y^{3}) \) **Expanded:** \( 8x^{8} - 16x^{4}y^{3} + 6y^{5}x^{4} - 12y^{8} \) These results provide the expanded forms of the given expressions. If you need further assistance or explanations, feel free to ask!