Question

Check with proof whether x2 - 4x + 4 is a perfect square​

Answer 1

Answer:

Yes, it is perfect square

Answer 2

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$\underline\bold\green{method \: 1}$

${x}^{2} - 4x + 4$

${x}^{2} - 2x - 2x + 4$

$x(x - 2) - 2(x - 2)$

$(x - 2)(x - 2)$

$(x - 2) {}^{2}$

$\underline \bold \green{method \: 2}$

${x}^{2} - 4x + 4$

${(x)}^{2} - 2(2)(x) + {(2)}^{2}$

$\pink{ \boxed{(a - b) {}^{2} = {a}^{2} - 2ab + {b}^{2}} }$

$(x - 2) {}^{2}$

Hence, the number is a perfect square.

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