Question

Find the product of (x + 5)(x − 5).

x2 − 10x + 25
x2 + 10x + 25
x2 − 25
x2 + 25

Answer 1

Answer: x^2 - 25

Step-by-step 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.

Answer 2

x^2 -25
All I did was divide both and I got the answer.