Factorise:
$(y^{3} - 3 y^{2} + 2 y - 6 - x y + 3 x)$

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Solution

Given:
$y^{3} - 3 y^{2} + 2 y - 6 - x y + 3 x$
$= (y^{3} - 3 y^{2}) + (2 y - 6) + (- x y + 3 x)$ , {group pair of terms}
$= y^{2} (y - 3) + 2 (y - 3) - x (y - 3)$ , {factor each binomials}
$= (y - 3) (y^{2} + 2 - x)$ , {factor out common factor $(y - 3)$ }

The common factors of $y^{3} - 3 y^{2} + 2 y - 6 - x y + 3 x$ are
$(y - 3) (y^{2} + 2 - x)$

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Factorise:

(i) ; (ii) ; (iii) ;

(iv)

y^{3} - 3 y^{2} + 2 y - 6 - x y + 3 x

Factorize:

$y^{3} - 3 y^{2} + 2 y - 6 - x y + 3 x$

(3 x + 2 y + x y + 6)

(y + 3)

Find the sum:

$(v i)$ $3 x + 4 x y - y^{2}, x y - 4 x + 2 y^{2}$ and $3 y^{2} - x y + 6 x$

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