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15 October, 20:43

Solve (2a^x+1/2b^x) ^2

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  1. 15 October, 21:29
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    Simplify 1/2b^x to b^x/2

    (2a^x + b^x/2) ^2

    Use the Square of Sum: (a + b) ^2 = a^2 + 2ab + b^2

    (2a^x) ^2 + 2 * 2a^x * b^x/2 + (b^x/2) ^2

    Use the Multiplication Distributive Property: (xy) ^a = x^a y^a

    2^2 (a^x) ^2 + 2 * 2a^x * b^x/2 + (b^x/2) ^2

    Simplify 2^2 to 4

    4 (a^x) + 2 * 2a^x * b^x/2 + (b^x/2) ^2

    Use the Power Rule: (x^a) ^b = x^ab

    4a^x * 2 + 2 * 2a^x * b^x/2 + (b^x/2) ^2

    Regroup terms

    4a^2x + 2 * 2a^x * b^x/2 + (b^x/2) ^2

    Use Division Distributive Property: (x/y) ^a = x^a/y^a

    4a^2x + 2 * 2a^x * b^x/2 + (b^x) ^2/2^2

    Use the Power Rule: (x^a) ^b = x^ab

    4a^2x + 2 * 2a^x * b^x/2 + b^x * 2/2^2

    Regroup terms

    4a^2x + 2 * 2a^x * b^x/2 + b^2x/2^2

    Simplify 2^2 to 4

    4a^2x + 2 * 2a^x * b^x/2 + b^2x/4

    Simplify 2 * 2a^x * b^x/2 to 4a^xb^x/2

    4a^2x + 4a^xb^x/2 + b^2x/4

    Simplify 4a^xb^x/2 to 2a^xb^x

    = 4a^2x + 2a^xb^x + b^2x/4
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