Find the product : $(2 x - 3 y) (2 x + 3 y) (4 x^{2} + 9 y^{2})$

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Solution

As we know the formula $(a + b) (a + b)$ = $a^{2} + b^{2}$
Similarly $(a - b) (a + b)$ = $a^{2} - b^{2}$
So = $(2 x - 3 y) (2 x + 3 y)$ = $(2 x)^{2} - (3 y)^{2}$
= $4 x^{2} - 9 y^{2}$ ... ( $e q 1$ )
So = $(4 x^{2} - 9 y^{2}) (4 x^{2} - 9 y^{2})$ .. using $(e q 1)$
= $(4 x^{2})^{2} - (9 y^{2})^{2}$
= $16 x^{4} - 81 y^{4}$

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