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Identity (x+y)(x-y)

Factorize2 x+...

Question

Factorize
(2x+3y)³ - (2x-3y)³

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Solution

Use the identity: a³ - b³ = (a - b)(a² + ab + b²)

(2x+3y)³ - (2x-3y)³
= [(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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Similar questions

Q. The value of

(2 x + 3 y)^{3} - (2 x - 3 y)^{3}

$(2 x - 3 y)^{3} + (x + 3 y)^{3} + 3 (2 x - 3 y)^{2} (x + 3 y) + 3 (2 x - 3 y) (x + 3 y)^{2} =$

Q. The value of

(2 x + 3 y)^{3} - (2 x - 3 y)^{3}

Q. The expression

(2 x - 3 y)^{3} + (x + 3 y)^{3} + 3 (2 x - 3 y)^{2} (x + 3 y) + 3 (2 x - 3 y) (x + 3 y)^{2} =

(2 x - 3 y)^{3}

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