Question

How do you multiply `(8x – 5)(4x – 7)`?

Answer 1

`32x^2-76x+35`

Explanation:

`"each term in the second factor is multiplied by each"`
`"term in the first factor"`

`rArr(color(red)(8x-5))(4x-7)`

`=color(red)(8x)(4x-7)color(red)(-5)(4x-7)`

`=(color(red)(8x)xx4x)+(color(red)(8x)xx-7)+(color(red)(-5)xx4x)+(color(red)(-5)xx-7)`

`=32x^2+(-56x)+(-20x)+35larrcolor(blue)"collect like terms"`

`=32x^2color(magenta)(-56x)color(magenta)(-20x)+35`

`=32x^2-76x+35`

Answer 2

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:

`32x^2-56x-20x+35`

Combine like terms:

`32x^2-76x+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.