Evaluate $105 \times 106$ without multiplying directly.
$11130$
$10030$
$11120$
$12130$
$105 \times 106=(100+5) \times(100+6)$
$=(100)^{2}+(5+6)(100)+(5 \times 6),$ using Identity $IV$
$=10000+1100+30$
$=11130$
Factorise $8 x^{3}+27 y^{3}+36 x^{2} y+54 x y^{2}$
Factorise : $x^{3}-2 x^{2}-x+2$
Verify : $x^{3}-y^{3}=(x-y)\left(x^{2}+x y+y^{2}\right)$
Factorise $x^{3}-23 x^{2}+142 x-120$
Factorise $4 x^{2}+y^{2}+z^{2}-4 x y-2 y z+4 x z$.
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