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Method of Intervals

How 12 x squa...

Question

How $12 x$ square $+ 7 x y - 12 y$ square equal to $(3 x + 4 y) \times (4 x - 3)$ ?

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Solution

Lets write the first given expression mathematically,
$12 x$ square $+ 7 x y - 12 y$ square $= 12 x^{2} + 7 x y - 12 y^{2}$
And we need to prove $12 x^{2} + 7 x y - 12 y^{2} = (3 x + 4 y) (4 x - 3)$
Lets consider the expression written on right side,
$R H S$
$= (3 x + 4 y) \times (4 x - 3)$
$= 3 x \times (4 x) - (3 x) \times (3) + (4 y) \times (4 x) + (4 y) \times (- 3)$
$= 12 x^{2} - 9 x + 16 x y - 12 y = L H S$
Hence, $12 x$ square $+ 7 x y - 12 y$ square equal to $(3 x + 4 y) \times (4 x - 3)$ .

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