Question

How do you foil `(9x + 7)(6x + 4)`?

Answer 1

`54x^2+78x+28`

Explanation:

FOIL stands for: First (times First), Outside (times Outside), Inside (times Inside), Last (times Last).

In the problem to expand `(9x+7)(6x+4)`, First-times-First is `9x * 6x = 54x^2`, Outside-times-Outside is `9x * 4 = 36x`, Inside-times-Inside is `7 * 6x=42x`, and Last-times-Last is `7 * 4=28`.

Combining these gives `(9x+7)(6x+4)=54x^2+36x+42x+28`. The `36x` and `42x` are "like terms" and combine to give `36x+42x=78x`. Therefore, the answer is:

`(9x+7)(6x+4)=54x^2+78x+28`

The reason this works is the distributive property: `a*(b+c)=a*b+a*c`, and the commutative property: `a*b=b*a`

`(a+b)*(c+d)=(a+b)*c+(a+b)*d`

`=a*c+b*c+a*d+b*d`

`=a*c+a*d+b*c+b*d` (which is what you'd get by using "FOIL" on the original product)