Question

(3xy-2ab)3_(3xy+2ab)³ simplify
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Answer 1

Given -

• (3xy - 2ab)³ - (3xy + 2ab)³

Solution -

• Method ➊

Apply identity

• a³ - b³ = (a - b)(a² + ab + b²)

→ [(3xy - 2ab) - (3xy + 2ab)][(3xy - 2ab)² + (3xy - 2ab)(3xy + 2ab) + (3xy + 2ab)³]

Apply identity

• (a - b)² = a² - 2ab + b²
• (a + b)² = a² + 2ab + b²
• a² - b² = (a + b)(a - b)

→ [3xy - 2ab - 3xy - 2ab][(3xy)² - 2 × 3xy × 2ab + (2ab)² + (3xy)² - (2ab)² +(3xy)² + 2 × 3xy × 2ab + (2ab)²]

→ [-2ab - 2ab][9x²y² - 12xyab + 4a²b² + 9x²y² - 4a²b² + 9x²y² + 12xyab + 4a²b²]

→ -4ab[9x²y² + 9x²y² + 9x²y² - 12xyab + 12xyab + 4a²b² - 4a²b² + 4a²b²]

→ - 4ab[27x²y² + 4a²b²]

→ - 108x²y²ab - 16a³b³

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• Method ➋

Apply identity

• (a - b)³ = a³ - b³ - 3ab(a - b)
• (a + b)³ = a³ + b³ + 3ab(a + b)

→ (3xy - 2ab)³

→ (3xy)³ - (2ab)³ - 3 × 3xy × 2ab(3xy - 2ab)

→ 27x³y³ - 8a³b³ - 18xyab(3xy - 2ab)

→ 27x³y³ - 8a³b³ - 54x²y²ab + 36xya²b² (i)

So,

→ (3xy + 2ab)³

→ (3xy)³ + (2ab)³ + 3 × 3xy × 2ab(3xy + 2ab)

→ 27x³y³ + 8a³b³ - 18xyab(3xy - 2ab)

→27x³y³ + 8a³b³+ 54x²y²ab + 36xya²b² (ii)

• Subtract (i) and (ii)

→ (27x³y³ - 8a³b³ - 54x²y²ab + 36xya²b²) - (27x³y³ + 8a³b³ + 54x²y²ab + 36xya²b²)

→ 27x³y³ - 8a³b³ - 54x²y²ab + 36xya²b² - 27x³y³ - 8a³b³ - 54x²y²ab - 36xya²b²

→ 27x³y³ - 27x³y³ - 8a³b³ - 8a³b³ - 54x²y²ab - 54x²y²ab + 36xya²b² - 36xya²b²

→ - 16a³b³ - 108x²y²ab

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Answer 2

Answer:

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