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

Question

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

UpStudy AI · Accepted Answer

Simplify the expression by following steps:
- step0: Multiply the terms:
  $$\left(x-5ight)\left(x-2ight)$$
- step1: Apply the distributive property:
  $$x	imes x-x	imes 2-5x-\left(-5	imes 2ight)$$
- step2: Multiply the terms:
  $$x^{2}-2x-5x-\left(-10ight)$$
- 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:
  $$\left(3x-1ight)\left(2x+3ight)$$
- step1: Apply the distributive property:
  $$3x	imes 2x+3x	imes 3-2x-3$$
- 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:
  $$\left(x-5ight)\left(x+3ight)$$
- step1: Apply the distributive property:
  $$x	imes x+x	imes 3-5x-5	imes 3$$
- 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:
  $$-3v\left(3a^{3}-6a^{2}+aight)$$
- step1: Rewrite the expression:
  $$-3\left(3a^{3}-6a^{2}+aight)v$$
- step2: Multiply the expression:
  $$-3\left(3a^{3}v-6a^{2}v+avight)$$
- 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:
  $$\left(x+5ight)\left(x-2ight)$$
- step1: Apply the distributive property:
  $$x	imes x-x	imes 2+5x-5	imes 2$$
- 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:
  $$\left(7m-2\pi ight)\left(3m+4night)$$
- step1: Apply the distributive property:
  $$7m	imes 3m+7m	imes 4n-2\pi 	imes 3m-2\pi 	imes 4n$$
- 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:
  $$\left(2x^{4}-3y^{2}ight)\left(3x^{4}+2y^{2}ight)$$
- step1: Apply the distributive property:
  $$2x^{4}	imes 3x^{4}+2x^{4}	imes 2y^{2}-3y^{2}	imes 3x^{4}-3y^{2}	imes 2y^{2}$$
- 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:
  $$\left(4x^{4}+3y^{5}ight)\left(2x^{4}-4y^{3}ight)$$
- step1: Apply the distributive property:
  $$4x^{4}	imes 2x^{4}-4x^{4}	imes 4y^{3}+3y^{5}	imes 2x^{4}-3y^{5}	imes 4y^{3}$$
- 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:
  $$\left(x+3ight)$$
- step1: Remove the parentheses:
  $$x+3$$
Expand the expression $$ (x+5)(x+3) $$
Simplify the expression by following steps:
- step0: Multiply the terms:
  $$\left(x+5ight)\left(x+3ight)$$
- step1: Apply the distributive property:
  $$x	imes x+x	imes 3+5x+5	imes 3$$
- 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!
Here are the expanded and simplified results for each expression: 1. $$ (x+3) = x + 3 $$ 2. $$ -3v(3a^{3}-6a^{2}+a) = -9a^{3}v + 18a^{2}v - 3av $$ 3. $$ (x+5)(x+3) = x^{2} + 8x + 15 $$ 4. $$ (x-5)(x-2) = x^{2} - 7x + 10 $$ 5. $$ (x+5)(x-2) = x^{2} + 3x - 10 $$ 6. $$ (x-5)(x+3) = x^{2} - 2x - 15 $$ 7. $$ (3x-1)(2x+3) = 6x^{2} + 7x - 3 $$ 8. $$ (7m-2\pi)(3m+4n) = 21m^{2} + 28mn - 6\pi m - 8\pi n $$ 9. $$ (2x^{4}-3y^{2})(3x^{4}+2y^{2}) = 6x^{8} - 5x^{4}y^{2} - 6y^{4} $$ 10. $$ (4x^{4}+3y^{5})(2x^{4}-4y^{3}) = 8x^{8} - 16x^{4}y^{3} + 6y^{5}x^{4} - 12y^{8} $$

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