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Find the value of a if $4a^2-16a+16$.
The given equation is $4a^2 - 16a + 16$.
We have to find the value of a.
$4a^2 – 16a + 16 = 0$
$4(a^2 – 4a + 4) = 0$ (taking 4 as a common in the equation)
$a^2 – 4a + 4 = 0$ (dividing 0 by 4 gives 0)
$a^2 – 2a – 2a + 4 = 0$ (using prime factorization)
$a(a – 2) – 2(a – 2) = 0$
$(a – 2) (a – 2) = 0$
$(a – 2)^2 = 0$
$a-2=0$
$a = 2$
The value of a is 2.
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