How do you multiply (8x – 5)(4x – 7)?

May 6, 2018

$32 {x}^{2} - 76 x + 35$

Explanation:

$\text{each term in the second factor is multiplied by each}$
$\text{term in the first factor}$

$\Rightarrow \left(\textcolor{red}{8 x - 5}\right) \left(4 x - 7\right)$

$= \textcolor{red}{8 x} \left(4 x - 7\right) \textcolor{red}{- 5} \left(4 x - 7\right)$

$= \left(\textcolor{red}{8 x} \times 4 x\right) + \left(\textcolor{red}{8 x} \times - 7\right) + \left(\textcolor{red}{- 5} \times 4 x\right) + \left(\textcolor{red}{- 5} \times - 7\right)$

$= 32 {x}^{2} + \left(- 56 x\right) + \left(- 20 x\right) + 35 \leftarrow \textcolor{b l u e}{\text{collect like terms}}$

$= 32 {x}^{2} \textcolor{m a \ge n t a}{- 56 x} \textcolor{m a \ge n t a}{- 20 x} + 35$

$= 32 {x}^{2} - 76 x + 35$

May 6, 2018

The F.O.I.L. method works well for multiplying two binomials but I prefer using the distributive property because it can be used to multiply polynomials of any size.

Explanation:

Given: (8x – 5)(4x – 7)

Use the distributive property to distribute the first factor across the second factor:

8x(4x – 7) – 5(4x – 7)

Use the distributive property, again, to multiply through the parentheses:

$32 {x}^{2} - 56 x - 20 x + 35$

Combine like terms:

$32 {x}^{2} - 76 x + 35$

This method produces the same results as the F.O.I.L. method but it, unlike the F.O.I.L method, can be used for polynomials of any size.