Factorize the given expressions:

(i) $- 4 a^{2} + 4 a b - 4 c a$

(ii) $x^{2} y z + x y^{2} z + x y z^{2}$

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Solution

Factorisation:

(i) $4 a^{2} = 2 \times 2 \times a \times a$

$4 a b = 2 \times 2 \times a \times b$

$4 c a = 2 \times 2 \times c \times a$

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

$= 2 \times 2 \times a [- (a) + b - c]$

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

(ii) $x^{2} y z = x \times x \times y \times z$

$x y^{2} z = x \times y \times y \times z$

$x y z^{2} = x \times y \times z \times z$

$∴ x^{2} y z + x y^{2} z + x y z^{2} =$ $(x \times x \times y \times z) + (x \times y \times y \times z) + (x \times y \times z \times z)$

$= x \times y \times z [x + y + z]$

$= x y z (x + y + z)$

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