How do I multiply more than two binomials?
Something like: (a+bx)^3 (not necessarily cubed, though).
I know to use FOIL, but I don't know how to use it when there's more than two binomials...
Sorry that I don't have any actual numbers to work with.
To multiply more than two binomials, you can use a method called the distributive property. While the FOIL method is helpful for multiplying two binomials, it can become more complex when there are more than two binomials involved.
Let's take the example you provided: (a + bx)^3. To expand this expression, you need to multiply each term of the first binomial by each term of the second binomial, and then multiply the result by each term of the third binomial.
Here's how you can do it step by step:
Step 1: Start by multiplying the first binomial by the second binomial using the distributive property.
(a + bx)(a + bx) = a(a) + a(bx) + bx(a) + bx(bx)
Simplifying this gives you: a^2 + abx + abx + b^2x^2
Step 2: Now you need to multiply the result from the previous step by the third binomial. To do this, once again use the distributive property.
(a^2 + abx + abx + b^2x^2)(a + bx) = a^2(a) + a^2(bx) + abx(a) + abx(bx) + abx(a) + abx(bx) + b^2x^2(a) + b^2x^2(bx)
Simplifying this further results in: a^3 + a^2bx + a^2bx + ab^2x^2 + a^2bx + ab^2x^2 + ab^2x^2 + b^3x^3
Step 3: Combine like terms, rearrange the terms in descending order of powers, and simplify the expression.
a^3 + 3a^2bx + 3ab^2x^2 + b^3x^3
And that's the expanded form of (a + bx)^3!
Remember, you can use this method for any number of binomials. Just apply the distributive property multiple times until you've multiplied every term from each binomial. Make sure to combine like terms and simplify the expression at the end.