Question : The simplified form of $(x+3)^{2}+(x-1)^{2}$ is:
Option 1: $(x^{2}+2x+5)$
Option 2: $2(x^{2}+2x+5)$
Option 3: $(x^{2}-2x+5)$
Option 4: $2(x^{2}-2x+5)$
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Correct Answer: $2(x^{2}+2x+5)$
Solution :
$(x+3)^{2} = x^{2} + 6x + 9$
$(x-1)^{2} = x^{2} - 2x + 1$
Adding these two expressions together, we get,
$(x+3)^{2}+(x-1)^{2}$
= $x^{2} + 6x + 9 + x^{2} - 2x + 1$
= $2x^{2} + 4x + 10 $
= $2(x^{2} + 2x + 5)$
Hence, the correct answer is $2(x^{2} + 2x + 5)$.
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