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Factorise. 81x⁴-16y⁴

User Wazner
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1 Answer

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(9x² + 4y²)(3x + y)(3x - y)

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It's a simple example of a difference of two squares.

Firstly, we can write the expression as a square minus another square in the form a²- b² which is (9x²)² - (4y²)².

The difference of squares can be factorized using the formula:

  • a² - b² = (a + b)(a - b)

Applying this to our expression, the factorized form will be:

  • (9x² + 4y²)(9x² - 4y²)

The resulting factor, 9x² - 4y², can be further factorized as it's also a difference of squares.

The final expression is:

  • (9x² + 4y²)(3x + y)(3x - y)

User Markus Rudel
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