Perform the indicated operations. Simplify your answer!
1. 2ab ( 4a² + 3ab - 7b²) = 8a³b + 6a²b² - 14ab³
2. -3xy (x³y³ - 3x²y + 7xy²) = -3x⁴y⁴ + 9x³y² - 21x²y³
3. (x + 2)(x² - 3x + 2) = x³ - x² - 4x + 4
4. (2x - 1)(2x² + 4x + 3) = 4x³ + 6x² + 2x - 3
5. (12y² - 9y + 16) (8y³ - 14y + 5) = 96y⁵ - 72y⁴ - 40y³ + 186y² - 269y + 80
6. (25a⁵b³c) ÷ (5ab⁴c) = 5a⁴b⁻¹
7. (16a³b²c⁵ - 24a⁵bc⁴ + 44a⁷b⁶c⁶) ÷ (4a²bc³) = ac(4bc - 6a² + 11a⁴b⁵c²)
8. (30c² + 19ac - 63a²) ÷ (6c - 7a) = 5c + 9a
9. (a⁶ + b⁶) + (a² + b²) = a²(a⁴ + 1) + b²(b⁴ + 1)
10. (6w³ + 7w² - 12w + 15) ÷ (2w² + 3w - 5) = (3w - 1) + [tex]\frac{6w + 10}{2w^2 + 3w - 5}[/tex]
Step-by-step explanation:
Given:
1. 2ab ( 4a² + 3ab - 7b²)
2. -3xy (x³y³ - 3x²y + 7xy²)
3. (x + 2)(x² - 3x + 2)
4. (2x - 1)(2x² + 4x + 3)
5. (12y² - 9y + 16) (8y³ - 14y + 5)
6. (25a⁵b³c) ÷ (5ab⁴c)
7. (16a³b²c⁵ - 24a⁵bc⁴ + 44a⁷b⁶c⁶) ÷ (4a²bc³)
8. (30c² + 19ac - 63a²) ÷ (6c - 7a)
9. (a⁶ + b⁶) + (a² + b²)
10. (6w³ + 7w² - 12w + 15) ÷ (2w² + 3w - 5)
Question:
Perform the indicated operations. Simplify your answer!
Solutions:
1. 2ab ( 4a² + 3ab - 7b²)
= 8a³b + 6a²b² - 14ab³
2. -3xy (x³y³ - 3x²y + 7xy²)
= -3x⁴y⁴ + 9x³y² - 21x²y³
3. (x + 2)(x² - 3x + 2)
= x³ - 3x² + 2x + 2x² - 6x + 4
= x³ - x² - 4x + 4
4. (2x - 1)(2x² + 4x + 3)
= 4x³ + 8x² + 6x - 2x² - 4x - 3
= 4x³ + 6x² + 2x - 3
5. (12y² - 9y + 16) (8y³ - 14y + 5)
= 96y⁵ - 168y³ + 60y² - 72y⁴ + 126y² - 45y + 128y³ - 224y + 80
= 96y⁵ - 72y⁴ - 40y³ + 186y² - 269y + 80
6. (25a⁵b³c) ÷ (5ab⁴c)
= 5a⁴b⁻¹
7. (16a³b²c⁵ - 24a⁵bc⁴ + 44a⁷b⁶c⁶) ÷ (4a²bc³)
= (16a³b²c⁵) ÷ (4a²bc³) - (24a⁵bc⁴) ÷ (4a²bc³) + (44a⁷b⁶c⁶) ÷ (4a²bc³)
= 4abc² - 6a³c + 11a⁵b⁵c³
= ac(4bc - 6a² + 11a⁴b⁵c²)
8. (30c² + 19ac - 63a²) ÷ (6c - 7a)
= (6c - 7a)(5c + 9a) ÷ (6c - 7a)
= 5c + 9a
9. (a⁶ + b⁶) + (a² + b²)
= a⁶ + b⁶ + a² + b²
= a⁶ + a² + b⁶ + b²
= a²(a⁴ + 1) + b²(b⁴ + 1)
10. (6w³ + 7w² - 12w + 15) ÷ (2w² + 3w - 5)
= (3w - 1)(2w² + 3w - 5) ÷ (2w² + 3w - 5) + [tex]\frac{6w + 10}{2w^2 + 3w - 5}[/tex]
= (3w - 1) + [tex]\frac{6w + 10}{2w^2 + 3w - 5}[/tex]
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- Theory about Perform the indicated operation, then simplify: https://brainly.ph/question/6905770
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