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 \(x_{1}\) by \(x_{2}\)
x x = \(x^{2}\)
2. (x + 5)(x - 5) Multiply \(x_{1}\) by -5 in the second binomial
x -5 = -5x
3. (x + 5)(x - 5) Multiply 5 in the first binomial to \(x_{2}\)
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.
\(x^{2}\) - 5x + 5x - 25
6. -5x and 5x cancel each other out when combining like terms so you're left with.
\(x^{2}\) - 25
In the end, steps 2, 3, 5, and 6. can be taken out by doing this.
Just multiply \(x_{1}\) by \(x_{2}\) to get \(x^{2}\)
Then just multiply 5 in the first binomial to -5 in the second binomial to get -25
Then write your answer.
\(x^{2}\) - 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.
