# How do you foil (2x+5)(4x-3)?

Aug 8, 2015

$8 {x}^{2} + 14 x - 15$

#### Explanation:

Evaluating the product of two binomials using FOIL:

Sum
$\textcolor{w h i t e}{\text{XXXX}}$product of First terms
$\textcolor{w h i t e}{\text{XXXX}}$product of Outside terms
$\textcolor{w h i t e}{\text{XXXX}}$product of Inside terms
$\textcolor{w h i t e}{\text{XXXX}}$product of Last terms

For the given example: $\left(2 x + 5\right) \left(4 x - 3\right)$
$\textcolor{w h i t e}{\text{XXXX}}$First terms: $2 x , 4 x$$\textcolor{w h i t e}{\text{XXXX}}$Product $= 8 {x}^{2}$
$\textcolor{w h i t e}{\text{XXXX}}$Outside terms: $2 x , - 3$$\textcolor{w h i t e}{\text{XXXX}}$Product $= - 6 x$
$\textcolor{w h i t e}{\text{XXXX}}$Inside terms: $5 , 4 x$$\textcolor{w h i t e}{\text{XXXX}}$Product $= 20 x$
$\textcolor{w h i t e}{\text{XXXX}}$Last terms: 5, -3color(white)("XXXX")#Product $= - 15$

Sum
$\textcolor{w h i t e}{\text{XXXX}}$$= 8 {x}^{2} - 6 x + 20 x - 15$

$\textcolor{w h i t e}{\text{XXXX}}$$= 8 {x}^{2} + 14 x - 15$