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Mathematics
Kael Miller
14 May, 23:44
Solve (2a^x+1/2b^x) ^2
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Gael Cruz
15 May, 00:38
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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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