Question

Factorise 6xy - 4y + 6 - 9x.​

Answer 1

Solution:-

⠀

Step 1:- Check if there is a common factor among all terms. There is none.

Step 2:- Think a grouping. Notice that first two terms have a common factor 2y;

$\sf{6xy - 4y = 2y (3x - 2)}$⠀⠀⠀......(a)

★ What about the last two term?

Observe them. If you change their order to $\sf{-9x + 6}$, the factor $\sf{(3x - 2)}$ will come out;

$\sf{-9x + 6 = -3 (3x) + 3 (2)}$

⠀⠀⠀ ⠀ $\sf{= -3 (3x - 2)}$⠀⠀⠀⠀......(b)

Step 3:- Putting (a) and (b) together,

$\sf{6xy - 4y + 6 - 9x = 6xy - 4y -9x + 6}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ $\sf{= 2y (3x - 2) -3 (3x - 2)}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ $\sf{= (3x - 2) (2y - 3)}$

The factors of $\sf{(6xy - 4y + 6 - 9x)}$ are $\sf{(3x - 2)}$ and $\sf{(2y - 3)}$.

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