Question

Simplify:
(x+y+z)² -(x - y -z)²​

Answer 1

Answer:

$\huge\boxed{(x+y+z)^2-(x-y-z)^2=4xy+4xz}$

Step-by-step explanation:

Use

$a^2-b^2=(a-b)(a+b)$

$(x+y+z)^2-(x-y-z)^2\\\\=\left[x+y+z-\left(x-y-z\right)\right][x+y+z+(x-y-z)]\\\\=(x+y+z-x+y+z)(x+y+z+x-y-z)\\\\=(2y+2z)(2x)\qquad|\text{use the distributive property}\\\\=(2y)(2x)+(2z)(2x)=4xy+4xz$

Answer 2

Answer:

4(xy+ zx)

Step-by-step explanation:

${(x + y + z)}^{2} - {(x - y - z)}^{2}$

$= {x}^{2} + {y}^{2} + {z}^{2} + 2xy + 2yz + 2zx - ( {x}^{2} + {y}^{2} + {z}^{2} - 2xy + 2yz - 2zx)$

$= {x}^{2} + {y}^{2} + {z}^{2} + 2xy + 2yz + 2zx - {x}^{2} - {y}^{2} - {z}^{2} + 2xy - 2yz + 2zx$

$= 4xy + 4yz + 4zx = 4(xy + zx)$