Question

Factor the expression below: X^2-10x+25

Answer 1

$\textbf{ \underline{Using middle term splitting:}} \\ \\ {x}^{2} - 10x + 25 \\ = {x}^{2} - 5x - 5x + 25 \\ = x(x - 5) - 5(x - 5) \\ = (x - 5)(x - 5) \\ = {(x - 5)}^{2}$
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$\textbf{ \underline{Using identity: }} \underline{ {(a - b)}^{2} = {a}^{2} - 2ab + {b}^{2} }\\ \\ {x}^{2} - 10x + 25 \\ = {(x)}^{2} - 2 \times 5 \times x + {(5)}^{2} \\ = {(x - 5)}^{2}$