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Math Help - Polynomials

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    Member maybeline9216's Avatar
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    Polynomials

    How to factorise (a^4) - (7a^2 x b^2)- 18b^4??
    Can show me step by step??

    Btw, the answer is (a+3b)(a-3b)(a^2+2b^2)
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    Quote Originally Posted by maybeline9216 View Post
    How to factorise (a^4) - (7a^2 x b^2)- 18b^4??
    Can show me step by step??

    Btw, the answer is (a+3b)(a-3b)(a^2+2b^2)
    Let A = a^2 and B = b^2.

    So we have A^2 - 7AB - 18B^2.

    You should be able to factorise this by inspection...

    (A-9B)(A+2B)

    (a^2 - 9b^2)(a^2 + 2b^2)

    Now you have a Difference of Two Squares as the first factor. Factorising that gives

    (a + 3b)(a - 3b)(a^2 + 2b^2).
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