Question

(x+2)²-(y+2)²=(x-y)(x+y+k) Find k​

Answer 1

Answer:

$k = 4.$

Step-by-step explanation:

${(x + 2)}^{2} - {(y + 2)}^{2} = (x - y)(x + y + k) \\ \\ (x + 2 - y - 2)(x + 2 + y + 2) = (x - y)(x + y + k) \\ \\ (x - y)(x + y + 4) = (x - y)(x + y + k) \\ \\ x + y + 4 = x + y + k \\ \\ then \: \: \: k = 4.$

Answer 2

Answer:

(x+2)²-(y+2)²=(x-y)(x+y+k)

(x²+2x+4)-(y²+2y+4)=(x²+xy+kx-xy-y²-ky)

x²+2x+4-y²-2y-4=x²-y²+kx-ky

2x-2y=kx-ky

2(x-y)=k(x-y)

k=2