Find the product: $(a + 2) (a - 3) (a + 4)$

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Solution

The given binomials are $(a + 2)$ , $(a - 3)$ and $(a + 4)$ .

Firstly multiply the first and second term as follows:

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

Now multiply the resulting expression:

$(a^{2} - a - 6) (a + 4) = (a^{2} \times a) + (a^{2} \times 4) + (- a \times a) + (- a \times 4) + (- 6 \times a) + (- 6 \times 4)$
$= a^{3} + 4 a^{2} - a^{2} - 4 a - 6 a - 24 = a^{3} + 3 a^{2} - 10 a - 24$

Hence, $(a + 2) (a - 3) (a + 4) = a^{3} + 3 a^{2} - 10 a - 24$ .

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