Question

simplify (3xy-2ab)^3 - (3xy + 2ab)^3

Answer 1

$( {3xy - 2ab)}^{3} - {(3xy + 2ab)}^{3} \\ = ({(3xy)}^{3} + {( - 2ab)}^{3} + 3 \times ( {3xy)}^{2} \times (- 2ab) + 3 \times 3xy \times {( - 2ab)}^{2}) - ({(3xy)}^{3} + {( 2ab)}^{3} + 3 \times ( {3xy)}^{2} \times ( 2ab) + 3 \times 3xy \times {( 2ab)}^{2}) \\ = 27 {x}^{3} {y}^{3} - 8 {a}^{3} {b}^{3} - 54 {x}^{2} {y}^{2}ab + 36xy {a}^{2} {b}^{2} - (27 {x}^{3} {y}^{3} + 8 {a}^{3} {b}^{3} + 54 {x}^{2} {y}^{2}ab + 36xy {a}^{2} {b}^{2})\\ = 27 {x}^{3} {y}^{3} - 8 {a}^{3} {b}^{3} - 54 {x}^{2} {y}^{2}ab + 36xy {a}^{2} {b}^{2} - 27 {x}^{3} {y}^{3} - 8 {a}^{3} {b}^{3} - 54 {x}^{2} {y}^{2}ab - 36xy {a}^{2} {b}^{2} \\ = - 16{a}^{3} {b}^{3} - 108{x}^{2} {y}^{2}ab$

Answer 2

Answer:

Let us consider,

Here, a = 3xy – 2ab and b = 3xy + 2ab

By using the formula,

[a³ – b³ = (a – b) (a² + ab + b²)]

Let us simplify the given expression, we get

(3xy – 2ab)3 – (3xy + 2ab)3 = [(3xy – 2ab) – (3xy + 2ab)] [(3xy – 2ab)² + (3xy – 2ab) (3xy + 2ab) + (3xy + 2ab)²]

= (3xy – 2ab – 3xy – 2ab) [(9x²y² – 12xyab + 4a²b²) + (9x²y² – 4a²b²) + (9x²y² + 12xyab + 4a²b²)]

= (- 4ab) (9x²y² + 9x²y² + 9x²y² – 12xyab + 12xyab + 4a²b² – 4a²b² + 4a²b²)

= (- 4ab) (27 xy² + 4a²b²)

= -108x²y²ab – 16a³b³