How do you explain expansion of algebraic equation?

Answer 1

If the expression is in the form y(x + z), then it is very simple to expand but is easier to demonstrate with examples.

x(x + 1)

Multiply everything in the brackets by what is in front:

x2 + x

Example 2:

2x(3x - 5)

6x2 - 10x

Example 3:

2y(3x + 4z)

6xy + 8yz

If there are two brackets then it is slightly harder:

(x + 2)(x - 6)

This can be written as:

x(x - 6) + 2(x - 6)

Expand as before:

x2 - 6x + 2x - 12

Simplify:

x2 - 4x - 12

However, this takes quite a long time so it is easier just to multiply everything in the second set of brackets by everything in the first set.

If the x term has a number in front of it (a coefficient), then it is again slightly harder:

(2x + 1)(x + 2)

2x2 + x + 4x + 2

2x2 + 5x + 2

If there the expression is in the form (x + y)2, it is the same as (x + y)(x + y) so you can work it out in the same way. However, you can also simply square x and y and add x times y doubled. For example:

(x + 3)2 = x2 + 6x + 9

If the power is greater than 2, you use binomial expansion but this is quite advanced.