Answer: x^2 - 25
Explanation:
Here is a tip/ shortcut to multiplying binomials in the (a + b)(a - b) format.
The only things you have to look for is the factor of a * a and the factor of b * b.
The reason being, a * -b and b * a cancel each other out no matter what.
For example
1. (x + 5)(x - 5) Multiply [tex]x_{1}[/tex] by [tex]x_{2}[/tex]
x * x = [tex]x^{2}[/tex]
2. (x + 5)(x - 5) Multiply [tex]x_{1}[/tex] by -5 in the second binomial
x * -5 = -5x
3. (x + 5)(x - 5) Multiply 5 in the first binomial to [tex]x_{2}[/tex]
5 * x = 5x
4. (x + 5)(x - 5) Multiply 5 in the first binomial to -5 in the second binomial
5 * -5 = -25
5. Now that you have all of your answers, write your equation, in order, to look like this.
[tex]x^{2}[/tex] - 5x + 5x - 25
6. -5x and 5x cancel each other out when combining like terms so you're left with.
[tex]x^{2}[/tex] - 25
In the end, steps 2, 3, 5, and 6. can be taken out by doing this.
Just multiply [tex]x_{1}[/tex] by [tex]x_{2}[/tex] to get [tex]x^{2}[/tex]
Then just multiply 5 in the first binomial to -5 in the second binomial to get -25
Then write your answer.
[tex]x^{2}[/tex] - 25
This works because there is no need for steps 2,3,5, and 6 since they lead to the same outcome from doing steps 1 and 4.
