x2+16x-16= x2+2×x×112+1122-16-1122= x+1122-16+1144 {Using a2+b2+2ab = a+b2}= x+1122-24+1144= x+1122-25144= x+1122-5122= x+112+512x+112-512 {Using a2-b2 = a-ba+b}= x+612x-412= x+12x-13

x²+ 1/6x -1/6

x^{2} + \frac{1}{6} x - \frac{1}{6} = x^{2} + 2 \times x \times \frac{1}{12} + {(\frac{1}{12})}^{2} - \frac{1}{6} - {(\frac{1}{12})}^{2} = {(x + \frac{1}{12})}^{2} - (\frac{1}{6} + \frac{1}{144}) {Using (a^{2} + b^{2} + 2 a b) = {(a + b)}^{2}} = {(x + \frac{1}{12})}^{2} - \frac{24 + 1}{144} = {(x + \frac{1}{12})}^{2} - \frac{25}{144} = {(x + \frac{1}{12})}^{2} - {(\frac{5}{12})}^{2} = (x + \frac{1}{12} + \frac{5}{12}) (x + \frac{1}{12} - \frac{5}{12}) {Using a^{2} - b^{2} = (a - b) (a + b)} = (x + \frac{6}{12}) (x - \frac{4}{12}) = (x + \frac{1}{2}) (x - \frac{1}{3})

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x2 + 1/6x -1/6

x²+ 1/6x -1/6