To explore the multiplication of algebraic expressions lets work
through a few examples.
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