# How do you multiply: (a-5)(a^2+5a+25)?

Apr 27, 2015
• We know the identity
color(blue)(x^3 - y^3 = (x-y)(x^2+xy+y^2)

The expression given to us is in the form $\left(x - y\right) \left({x}^{2} + x y + {y}^{2}\right)$ where:
$x = a , \mathmr{and} y = 5$

Hence the expression can directly be written as a^3 - 5^3 = color(green)(a^3 - 125

• But if we are not familiar with the identity we can use the Distributive Property of Multiplication to solve this expression

$\left(a - 5\right) \left({a}^{2} + 5 a + 25\right)$

$a \cdot \left({a}^{2} + 5 a + 25\right) - 5 \left({a}^{2} + 5 a + 25\right)$

$= \left(a \cdot {a}^{2}\right) + \left(a \cdot 5 a\right) + \left(a \cdot 25\right) - \left(5 \cdot {a}^{2}\right) - \left(5 \cdot 5 a\right) - \left(5 \cdot 25\right)$

$= {a}^{3} + \cancel{5 {a}^{2}} + \cancel{25 a} - \cancel{5 {a}^{2}} - \cancel{25 a} - 125$

color(green)( = a^3 - 125