Question

Find the product of

$(a-3)(a-5)(a-7)$

Answer 1

$(a-3)(a-5)(a-7)$

$=[a+(-3\left)\right][a+(-5\left)\right][a+(-7\left)\right]$

$=a^3+(-3-5-7)a^2+\left[\right(-3\left)\right(-5)+(-5\left)\right(-7)+(-7\left)\right(-3\left)\right]a+(-3)(-5)(-7)$

$=a^3-15a^2+(15+35+21)a-105$

$=a^3-15a^2+71a-105$