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(5+7)(2+5)(5+\sqrt{7})(2+\sqrt{5})

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Full solution

Q. (5+7)(2+5)(5+\sqrt{7})(2+\sqrt{5})
  1. Apply Distributive Property: First, we'll use the distributive property (FOIL method) to multiply the two binomials.\newline(5+7)(2+5)=5⋅2+5⋅5+7⋅2+7⋅5(5+\sqrt{7})(2+\sqrt{5}) = 5\cdot 2 + 5\cdot \sqrt{5} + \sqrt{7}\cdot 2 + \sqrt{7}\cdot \sqrt{5}
  2. Multiply Terms: Now, let's multiply the terms.\newline5×2=105\times2 = 10, 5×5=555\times\sqrt{5} = 5\sqrt{5}, 7×2=27\sqrt{7}\times2 = 2\sqrt{7}, and 7×5=35\sqrt{7}\times\sqrt{5} = \sqrt{35}\newlineSo, (5+7)(2+5)=10+55+27+35(5+\sqrt{7})(2+\sqrt{5}) = 10 + 5\sqrt{5} + 2\sqrt{7} + \sqrt{35}
  3. Combine Like Terms: Combine the like terms if there are any; in this case, there are no like terms to combine.\newlineSo the expression is already simplified.\newline10+55+27+3510 + 5\sqrt{5} + 2\sqrt{7} + \sqrt{35} is the final answer.

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