Using the identity $(x + a) (x + b) = x^{2} + (a + b) x + a b$ , find the product of $(7 x + 3 y) (7 x - 3 y)$ .

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Solution

Given identity is $(x + a) (x + b) = x^{2} + (a + b) x + a b$
We need to use this identity to expand $(7 x + 3 y) (7 x - 3 y)$
Here $a = 3 y, b = - 3 y$
Thus we have $(7 x + 3 y) (7 x - 3 y) = (7 x)^{2} + [7 x (3 y - 3 y)] + 3 y (- 3 y)$
$= 49 x^{2} + 7 x \times 0 - 9 y^{2}$
$= 49 x^{2} - 9 y^{2}$

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