Question

k2 - 8k + 16 ? perfect square trinomial as the square of a binomial.

Answer 1

Answer:

k2 - 8k +16

= k2 - 4k - 4k + 16

= k (k - 4) -4(k-4)

= (k-4)(k+4)

k=4 , k-4

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Answer 2

Given,

$\[{k^2} - 8k + 16\]$

Solution,

Consider the polynomial is $\[a{x^2} + bx + c\]$

The solution,

$\[x = \frac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}\]$

Compare the given equation with standard equation,

$\[a = 1,b = - 8,c = 16\]$

$\[x = \frac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}\]$

$\[ \Rightarrow x = \frac{{ - \left( { - 8} \right) \pm \sqrt {{{\left( { - 8} \right)}^2} - 4 \times 1 \times 16} }}{{2 \times 1}}\]$

$\[ \Rightarrow x = \frac{{8 \pm \sqrt {64 - 64} }}{2}\]$

$\[\begin{array}{l} \Rightarrow x = \frac{8}{2}\\ \Rightarrow x = 4\end{array}\]$

Hence the value is 4.