Example

Multiply the following: x²(x³ + 5y)

Let’s start by multiplying everything inside the brackets by x2

= x6 + 5y x²
We can not simplify this equation any further, so we present our answer as it is.

Example

Let’s try another one:

Multiply the following: (4x +3)(y + 6)

First we take each term of the first bracket and multiply them by the second bracket:

(4x +3)(y + 6)
= 4x(y + 6) + 3(y + 6)

Next we expand each bracket:

(4x +3)(y + 6)
= 4x(y + 6) + 3(y + 6)
= 4xy + 24x + 3y + 18

We cannot simplify this answer any more since there are no like terms so we are done at this point.

Example

Let’s try one more:

Multiply (x – 6)²

Let’s start by expanding this problem as such:

(x – 6)²
= (x+6)(x+6)

Now let’s multiply the first bracket by the second bracket just like we did in our last example..

(x – 6)²
= (x+6)(x+6)
= x(x+6) + 6(x+6)
= x2 + 6x + 6x + 36

Notice we now have two like terms 6x and 6x so we can simplify this problem even more.

(x – 6)²
= (x+6)(x+6)
= x(x+6) + 6(x+6)
= x2 + 6x + 6x + 36
= x² + 12x + 36