What number must be subtracted from $25 p^{2} - 30 p + 12$ to make the expression a perfect square.

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Solution

Sol $^{n}$ Given eq $^{n}$ is $25 p^{2} - 30 p + 12$

we can easily see that it's an identify of

$(a - b)^{2} = a^{2} - 2 a b + b^{2} . . . (1)$

where $a = 5 p$ and $- 2 a t = - 30 p$

$\Rightarrow - 2 \times 5 p \times b = - 2. (5 p) .3$

[splitting $- 30 p$ to make it in the from of -2at]

$\Rightarrow b = 3$

So, $b^{2} = 9$ and we have $12$

So, we need to subtract $3$ from the eq $^{n}$

to make it a perfect square of $(5 p - 3)^{2}$

$\Rightarrow 25 p^{2} - 30 p + 12 - 3 = 25 p^{2} - 30 p + 9$

$= (5 p - 3)^{2}$ ${(1)}$

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