2. Multiplication of Algebraic Expressions
When we multiply algebraic expressions, we need to remember the Index Laws from the Numbers chapter.
Let's see how algebra multiplication works with a series of examples.
Multiply x3(x4 + 5a)
We expand this out using the distributive law:
x3(x4 + 5a)
= x7 + 5ax3
We cannot simplify this answer any further. We present our answer in alphabetical order since it makes it easier to read when the problems become more involved.
Multiply (x + 5)(a − 6)
We multiply this out as follows. We take each term of the first bracket and multiply them by the second bracket. Then we expand out the result.
(x + 5)(a − 6)
= x(a − 6) + 5(a − 6)
= ax − 6x + 5a − 30
We cannot do any more with this answer. There are no like terms, so we cannot simplify it in any way.
Multiply (2x + 3)(x2 − x − 5)
Multiply `(x - 3)^2`
`(x - 3)^2`
is NOT equal to
`x^2 - 9`
Please take note of this! Many students confuse this idea and it's not surprising because sometimes the way we write math is not consistent. (See also Towards more meaningful math notation for a discussion on this issue.)
Simplify 5x[−4 + 10(x − y)] + 7x