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? asked in Science & MathematicsMathematics · 5 years ago

factor 81x^4 - 256y^4?

So far I got (9x^2)^2 -(16y^2)^2, but I don't know what to do next

6 Answers

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  • lenpol7
    Lv 7
    5 years ago

    Factor again

    (9x^2 - 16y^2)(9x^2 + 16y^2)

    (3x - 4y)(3x+ 4y)(9x^2 + 16y^2)

    (3x - 4y)(3x + 4y)((3x)^2 + (4y)^2)

    NB

    Two squared terms with a plus(+) between does NOT factor) .

    However, two squared terms with a minus(-) does factor to (x - y)(x + y)

    Note the plus sign in the second brackets.

  • ?
    Lv 7
    5 years ago

    　

    You really should know by now how to factor a difference of squares:

    a² − b² = (a−b) (a+b)

    81x⁴ − 256y⁴

    = (9x²)² − (16y²)²

    = (9x²−16y²) (9x²+16y²)

    = ((3x)²−(4y)²) (9x²+16y²)

    = (3x−4y) (3x+4y) (9x²+16y²)

  • ?
    Lv 7
    5 years ago

    81x^4 - 256y^4

    = (9x^2 + 16y^2)(3x + 4y)(3x - 4y)

  • Como
    Lv 7
    5 years ago

    [ 9x^2 - 16 y^2 ] [ 9x^2 + 16y^2 ]

    [ 3x - 4y ] [ 3x + 4y ] [ 9x^2 + 16y^2 ]

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  • Bryce
    Lv 7
    5 years ago

    (9x²+16y²)(9x²-16y²)

    =(9x²+16y²)(3x+4y)(3x-4y)

  • DWRead
    Lv 7
    5 years ago

    a² - b² = (a+b) (a-b)

    81x⁴ - 256y⁴ = (9x²)² - (16y²)²

    = (9x² + 16y²) (9x² - 16y²)

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