Question

simplify (x+y+z)^2-(x+y-z)^2​

Answer 1

Answer:

Step-by-step explanation:

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

= x^2 + y^2 + z^2 + 2xy + 2yz + 2zx

+ x^2 + y^2 + z^2 + 2xy - 2yz - 2zx

= 2x^2 + 2y^2 + 2z^2 + 4xy

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

Answer 2

(x+y+z)² - (x+y-z)²

Here,

• Terms are as a² - b² which can be factored as (a + b)(a - b)

So,

$\bf(x+y+z)^2-(x+y-z)^2 \\ \small \tt\{(x+y+z) + (x+y-z) \} \{ (x+y+z) - (x+y-z)\} \\ \small \rm \{x + y +\cancel{z} + x + y - \cancel{z} \} \{\cancel{x} + \cancel{y} + z - \cancel{x} - \cancel{y} + z \} \\ \small \tt \{ x + x + y + y\} \{ z + z\} \\ \large \tt \{ \red{2x + 2y}\} \{ \red{2z}\}$