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Factorise: (2x+3y)³ - (2x-3y)³ |
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Answer» Use the IDENTITY: a³ - b³ = (a - b)(a² + AB + b²) = [(2x + 3y) - (2x-3y) ][(2x-3y)² + (2x - 3y)(2x + 3y) + (2x + 3y)² ] = [ 2x + 3y - 2x + 3y ][(4x² + 9y² - 12xy) + (4x² - 9y²) + (4x² + 9y² + 12xy) ] = [6y][ 4x² + 9y² - 12xy + 4x² - 9y² + 4x² + 9y² + 12xy ] = [6y][ 4x² + 4x² + 4x² + 9y² + 9y² - 9y² - 12xy + 12xy ] = [6y][ 12x² + 9y²] = 6y×3×(4x² + 3y²) = 18y(4x² + 3y²) |
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