Find the product: $(3 t + 1) (3 t + 4)$

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Solution

Using the formula $(x + a) (x + b)$ = $x^{2} + (a + b) x + a b$
Taking $x = 3 t$ $a = 1$ $b = 4$ and substitutig in the above formula we get: $(3 t + 1) (3 t + 4)$ = $(3 t)^{2} + (1 + 4) 3 t + (4) (1)$ $=$ $9 t^{2} + (5) 3 t + 4$
Hence the answer is $9 t^{2} + 15 t + 4$

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