Question

8. The product of two expressions is y2 - z2 + 2xy - 2xz. If one of them is 2x + y + z,
find the other​

Answer 1

Answer:

Let other expression be E

Then,

E = (y^2 - z^2 + 2xy - 2xz)/

(2x + y + z)

= [(y+z)(y-z) + 2x(y-z)]/

(2x + y + z)

= (2x + y + z)(y + z)/

(2x + y + z)

= (y + z)

Therefore other expression

= (y + z)

Answer 2

we can take y2 and z2 as a and b so ,

a2+b2=(a+b)(a-b)

and in 2xy and 2xy common 2x

$\frac{ {y}^{2} - {z}^{2} + 2xy - 2xz}{2x + y + z} \\ = \frac{(y + z)(y - z) + 2x(y - z)}{2x + y + z}$

= y-z