The factors of a^2-b^2-4c^2+4d^2-4(ad-bc) are

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The factors of a^2-b^2-4c^2+4d^2-4(ad-bc) are

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Hailey 2 months 2021-11-10T18:02:46+00:00 1 Answer 0 views 0

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    2021-11-10T18:04:12+00:00

     Given \:a^{2} - b^{2}-4c^{2} + 4d^{2} - 4(ad-bc)

     = \:a^{2} - b^{2}-4c^{2} + 4d^{2} - 4ad+ 4bc

    /* Rearranging the terms, we get */

     = a^{2} + 4d^{2} - 4ad - b^{2} - 4c^{2} + 4bc

     = (a^{2} + 4d^{2} - 4ad) - (b^{2} +4c^{2} -4bc )

     = [a^{2} + (2d)^{2} - 2\times a \times (2d)] - [b^{2} +(2c)^{2} - 2\times b \times (2c )]

     = ( a - 2d )^{2} - ( b - 2c)^{2}

     = [ (a-2d) + ( b - 2c ) ] [ (a-2d) - ( b - 2c ) ] \\= (a-2d+b-2c)(a-2d-b+2c) \\= ( a+b-2c-2d)(a-b+2c-2d)

    Therefore.,

     \red{a^{2} - b^{2}-4c^{2} + 4d^{2} - 4(ad-bc) }\\\green { = ( a+b-2c-2d)(a-b+2c-2d) }

    ♪•••

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