Evaluate the product of $(2 a + 3 b) (2 a - 3 b)$

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Solution

The given polynomials are $2 a + 3 b$ and $2 a - 3 b$ we multiply them as follows:

$(2 a + 3 b) (2 a - 3 b) = (2 a \times 2 a) + (2 a \times - 3 b) + (3 b \times 2 a) + (3 b \times - 3 b) = 4 a^{2} - 6 a b + 6 a b - 9 b^{2}$
$= 4 a^{2} - 9 b^{2}$

Hence, $(2 a + 3 b) (2 a - 3 b) = 4 a^{2} - 9 b^{2}$ .

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