Factorize the following:


Factorize the following:
−4a2 + 4ab − 4ca


The greatest common factor of the terms $-4 a^{2}, 4 a b$ and $-4 c a$ of the expression $-4 a^{2}+4 a b-4 c a$ is $-4 a$.

Also, we can write $-4 a^{2}=-4 a \times a, 4 a b=-4 a \times(-b)$ and $4 c a=-4 a \times c$.

$\therefore-4 a^{2}+4 a b-4 c a=-4 a \times a+(-4 a) \times(-b)-4 a \times c$

$=-4 a(a-b+c)$

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