# What term should be added to each of the following expressions to make it a perfect square?1. 4a.sq +28a2.36a.sq+49b.sq3.4a.sq+814.9a.sq+2ab+b.sq?

$Using\;formula: (a+b)^2=a^2+b^2+2ab\\*(a-b)^2=a^2+b^2-2ab\\* 1)\;4a^2+28a\\* \Rightarrow 4a^2=(2a)^2\\* \Rightarrow 28a=2(7)(2a)\\*so,\;49\; must\;be\;added\;to\; make\;it\;perfect\;square\\*\Rightarrow 4a^2+28a+49=(2a+7)^2\\* 2)\;36a^2+49b^2\\* \Rightarrow 36a^2=(6a)^2\\*\Rightarrow 49b^2=(7b)^2\\* So,\;84ab\;must \;be\;added\;to \;make\;it\;perfect\;square\\* \Rightarrow 36a^2+49b^2+84ab=(6a+7b)^2\\* 3)\;4a^2+81\\* \Rightarrow 4a^2 =(2a)^2\\*\Rightarrow 81=9^2\\* So,\;36a\;must\;be\;added\;to\;make\;it\;perfect\;square\\* \Rightarrow 4a^2+81+36a=(2a+9)^2\\* 4)\;9a^2+2ab+b^2%u200B\\* \Rightarrow 4ab\;must\;be\;added\;to\;make\;it\;perfect\;square\\* \Rightarrow 9a^2+6ab+b^2=(2a+b)^2$

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