Question

One of the factors of x² + y² + 2xy - z² is ?​

Answer 1

x + y + z.

Explanation:

x² + y² + 2xy - z²

= (x + y)^2 - z^2

This is the difference between 2 squares so the factors are:

(x + y + z) and (a + y - z).

Answer 2

Answer: The factors are (x+y+z) and (x+y-z)

In other words, it factors to (x+y+z)*(x+y-z)

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Work Shown:

`x^2 + y^2 + 2xy - z^2\\\\(x^2 + 2xy + y^2) - z^2\\\\(x+y)^2 - z^2\\\\(x+y+z)(x+y-z)\\\\`

Notes:

• In the third step, I used the rule (A+B)^2 = A^2+2AB+B^2. For this, A = x and B = y.
• In the last step, I used the difference of squares factoring rule A^2-B^2 = (A+B)(A-B). In this case, A = x+y and B = z.