Evaluate :
$(3 x - 4 y) (3 x + 4 y) (9 x^{2} + 16 y^{2})$

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Solution

Step 1 : Evaluate the given expression

Applying the formula of product of sum and difference of two terms:
$(3 x - 4 y) (3 x + 4 y) (9 x^{2} + 16 y^{2}) = [(3 x)^{2} - (4 y)^{2}] [9 x^{2} + 16 y^{2}]$
[Taking first two terms & using $(a + b) (a - b) = a^{2} - b^{2}]$
$= (9 x^{2} - 16 y^{2}) (9 x^{2} + 16 y^{2})$
$= (9 x^{2})^{2} - (16 y^{2})^{2}$ $[∵ (a + b) (a - b) = a^{2} - b^{2}]$
$= 81 x^{4} - 256 y^{4}$
Hence, $(3 x - 4 y) (3 x + 4 y) (9 x^{2} + 16 y^{2}) = 81 x^{4} - 256 y^{4}$

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