Question

all identities in x, y, z​

Answer 1

Step-by-step explanation:

1) ( x + y )2 = x2 + 2xy +y2

2) ( x – y) 2 = x2 – 2xy + y2

3) (x + y)(x – y) = x2 – y2

4) (x + a)(x + b) = x2 +(a + b)x + ab

5) (x + y) 3 = x3 + 3x2y + 3xy2 + y3 = x3 + y3 +3xy(x +y)

6) (x - y) 3 = x3 - 3x2y + 3xy2 - y3 = x3+ y3 -3xy(x –y)

7) (x + y + z) 2 = x2 + y2 + z2 + 2xy + 2yz + 2zx

8) x3 + y3 = (x + y)(x2 – xy + y2)

9) x3 - y3 = (x - y)(x2 + xy + y2)

10) x3 + y3 + z3 – 3xyz = (x + y + z)(x2 + y2 + z2 – xy – yz – zx)

If x + y + z = 0 , then x3 + y3 + z3 = 3xyz