Factories the following expressions.
(i) $7 x - 42$

(ii) $6 p - 12 q$
(iii) $7 a^{2} + 14 a$
(iv) $- 16 z + 20 z^{2}$
(v) $20 l^{2} m + 30 a l m$
(vi) $5 x^{2} y - 15 x y^{2}$
(vii) $10 a^{2} - 15 b^{2} + 20 c^{2}$
(viii) $- 4 a^{2} + 4 a b - 4 c a$
(ix) $x^{2} y z + x y^{2} z + x y z^{2}$
(x) $a x^{2} y + b x y^{2} + c x y z$

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Solution

To factories following expressions first take common on both side.
(i) $7 x - 42 = 7 (x - 6)$
(ii) $6 p - 12 q = 6 (p - 2 q)$
(iii) $7 a^{2} + 14 a$ $= 7 a (a + 2)$
(iv) $- 16 z + 20$ $z^{2} = 4 z (5 z^{2} - 4)$
(v) $20 l^{2} m + 30 a l m$ $= 2 l m (10 l + 15 a)$
(vi) $5 x^{2} y - 15 x y^{2} = 5 x (x y - 3 y^{2})$
(vii) $10 a^{2} - 15 b^{2} + 20 c^{2} = 5 (2 a^{2} - 3 b^{2} + 4 c^{2})$
(viii) $- 4 a^{2} + 4 a b - 4 c a$ $= - 4 a (a - b + c)$
(ix) $x^{2} y z + x y^{2} z + x y z^{2}$ $= x y z (x + y + z)$
(x) $a x^{2} y + b x y^{2} + c x y z$ $= x y (a x + b y + c z)$

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Similar questions

Factorise the following expressions

(i) 7x − 42

(ii) 6p − 12q

(iii) 7a² + 14a

(iv) −16z + 20z³

(v) 20l²m + 30 alm

(vi) 5x²y − 15xy²

(vii) 10a² − 15b² + 20c²

(viii) −4a² + 4ab − 4 ca

(ix) x²yz + xy²z + xyz²

(x) ax²y + bxy² + cxyz

Factorize the given expressions:

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

$i i .) x^{2} y z + x y^{2} z + x y z^{2}$

a x^{2} y + b x y^{2} + c x y z

a x^{2} y + b x y^{2} + c x y z

a x^{2} y + b x y^{2} + c x y z

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