When multiplying two first degree binomials of a single variable you will find a pattern in your results. In case you have forgotten how to multiply, this is an application of the distributive property.
Observe these four possibilities:
= x (x + 6) + 4 (x + 6) = x * x + x * 6 + 4 * x + 4 * 6 = x2 + 6x +4x + 24 = x2 + 10x + 24
= x (x + 6) - 4 (x + 6) = x * x + x * 6 - 4 * x - 4 * 6 = x2 + 6x - 4x - 24 = x2 + 2x - 24
= x ( x - 6) + 4 ( x - 6) = x * x - x * 6 + 4 * x - 4 * 6 = x2 - 6x + 4x - 24 = x2 - 2x - 24
= x (x - 6) - 4 (x - 6) = x * x - x * 6 - 4 * x + 4 * 6 = x2 - 6x - 4x + 24 = x2 - 10x +- 24
Often, this distributive process is referred to as F.O.I.L. which stands for First, Outside, Inside, Last. This process works whenever you multiply two bimonials. You find the product of the two First terms, then the product of the two Outside terms, then the product of the two Inside terms, then the product of the two Last terms. After that, simplify (combine like terms) by adding the two middle terms.
For the simple ones, however, we will use a shortcut.
Caution: In these examples we are only dealing with examples where both of the first terms are "x" (a coefficient of 1).*
If we had (2x+4)(x+6) the method would be different.
Notice that in the first one the sum of 4 and 6 is 10 and the product of 4 and 6 is 24.
Our result was: x2 + 10x + 24
Notice that in the second one the sum of -4 and 6 is 2 and the product of -4 and 6 is -24.
Our result was: x2 + 2x + 24
Notice that in the third one the sum of 4 and -6 is -2 and the product of 4 and -6 is -24.
Our result was: x2 - 2x - 24
Notice that in the last one the sum of -4 and -6 is -10 and the product of -4 and -6 is 24.
Our result was: x2 - 10x + 24
From this we can conclude that our answer will be a trinomial where the middle ("x") term has a coefficient that is the sum of the last terms of the binomials. The third term is the product of those last terms.
* So, we have learned that when x has a coefficient of 1, then
For (x + 2) (x + 5) the sum is 7 and the product is 10 so we get x2 + 7x + 10
For (x-2) (x + 5) the sum is 3 and the product is -10 so we get x2 + 3x - 10