Factorise the following expression: $4 x^{2} - 8 x + 4$

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Solution

Factorise the given expression by using identities
Given, $4 x^{2} - 8 x + 4$
We know that ${(a - b)}^{2} = a^{2} + b^{2} - 2 a b$
Now, compare the given expression with this identity, we get
$= 4 x^{2} - 8 x + 4 = {(2 x)}^{2} + {(2)}^{2} - (2 \times 2 x \times 2) = {(2 x - 2)}^{2}$
Therefore, $4 x^{2} - 8 x + 4$ can be factorised as ${(2 x - 2)}^{2}$ .

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Factorise:

$4 x^{2} + 8 x + 4$

1 . 49 y^{2} + 84 y z + 36 z^{2} 2 . 4 x^{2} - 8 x + 4 3 . 121 b^{2} - 88 b c + 16 c^{2}

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