In each case, state True if the trinomial is a perfect square else state False. $x^{2} - 4 x + 16$

True

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False

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Solution

The correct option is B False
For this trinomial to be a perfect square, we should be able to write it in the form of $a^{2} - 2 a b + b^{2}$
$x^{2} - 4 x + 16 = x^{2} - 2 \times (2 x) + 4^{2}$
The term $2 a b$ should have been, $16 x = 2 \times (2 x) \times (4)$ , for the given trinomial to be a perfect square.
Since, it cannot be written in the given format, it is not a perfect square.

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9 b^{2} + 12 b + 16

16 x^{2} - 16 x y + y^{2}

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In each case, find whether the trinomial is a perfect square or not :

$(i) x^{2} + 14 x + 49$ $(i i) a^{2} - 10 a + 25$

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$(v) 16 x^{2} - 16 x y + y^{2}$ $(v i) x^{2} - 4 x + 16$

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