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Question

Simplify: (2x+4)2(2-\sqrt{x+4})^2

Solution

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(2x+4)2=2222x+4+(x+4)2=44x+4+x+4=84x+4+x\begin{align*} (2-\sqrt{x+4})^{2} &=2^{2}-2\cdot2\sqrt{x+4}+(\sqrt{x+4})^{2}\\ &=4-4\sqrt{x+4}+x+4\\ &=8-4\sqrt{x+4}+x \end{align*}

Use special product formula for the square of a binomial.

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