How do you use FOIL to multiply (x+2)(6x+10) ?

Jun 29, 2015

$6 {x}^{2} + 22 x + 20$

Explanation:

FOIL stands for "First, Outside, Inside, Last".

When multiplying two binomials $\left(a + b\right) \cdot \left(c + d\right)$, the distributive and commutative laws are what ultimately allow you to say that the answer is the sum of "First times First" $a \cdot c$, "Outside times Outside" $a \cdot d$, "Inside times Inside" $b \cdot c$, and "Last times Last" $b \cdot d$.

Thus,

$\left(a + b\right) \cdot \left(c + d\right) = a c + a d + b c + b d$.

Again, the reason this is true is the distributive law (used twice) and the commutative law (in the last step), which allows you to write

$\left(a + b\right) \cdot \left(c + d\right) = \left(a + b\right) \cdot c + \left(a + b\right) \cdot d$

$= a \cdot c + b \cdot c + a \cdot d + b \cdot d = a c + a d + b c + b d$.

For the given problem, $a = x$, $b = 2$, $c = 6 x$, $d = 10$, so

$\left(x + 2\right) \left(6 x + 10\right) = 6 {x}^{2} + 10 x + 12 x + 20 = 6 {x}^{2} + 22 x + 20$.