Distributive Property

The distributive property states that:

A × (B + C) = AB + AC

This means that when you have a term multiplying a sum, you distribute that term to each part of the sum. Let's see a more complicated example:

(A + B)(C + D)

In this case, we will distribute both terms in the first set of parentheses to both terms in the second set:

A(C + D) + B(C + D)

Now, we distribute again:

AC + AD + BC + BD

So, the distributive property allows us to expand expressions by multiplying each term in one binomial with each term in the other binomial. Let's look at another example:

(2x + 3)(x + 4)

Distribute the terms:

2x(x + 4) + 3(x + 4)

Now distribute again:

2x² + 8x + 3x + 12

Finally, combine like terms:

2x² + 11x + 12

This process is essential when simplifying polynomials and expanding expressions in algebra.