Evaluate the following: (1+2 x )^5+(1-2 x )^5 - Vidyadip

Question

Evaluate the following:
$(1+2\sqrt{\text{x}})^5+(1-2\sqrt{\text{x}})^5$

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Answer

$(1+2\sqrt{\text{x}})^5+(1-2\sqrt{\text{x}})^5$
$=2\big[{^5\text{C}}_0+{^5\text{C}}_2\big(2\sqrt{\text{x}}\big)^2+{^5\text{C}}_4\big(2\sqrt{\text{x}}\big)^4\big]$
$=2\big[1+10\times4\times\text{x}+16\times\text{x}^2\times5\big]$
$=2+80\text{x}+160\text{x}^2$

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