Question

(×+y+z)^2
need help asap​

Answer 1

x² + y² + z² +2xy + 2xz + 2yz

Explanation:

(x + y + z)² = (x + y + z)(x + y + z)

Each term in the second factor is multiplied by each term in the first factor, that is

x(x + y + z) + y(x + y + z) + z(x + y + z) ← distribute parenthesis

= x² + xy + xz + xy + y² + yz + xz + yz + z² ← collect like terms

= x² + y² + z² + 2xy + 2xz + 2yz

Answer 2

`\large\boxed{(x+y+z)^2=x^2+y^2+z^2+2xy+2xz+2yz}`

Explanation:

Why?

Let y + z = t. Then

`x+y+z=x+t\to(x+y+z)^2=(x+t)^2`

Use

`(a+b)^2=a^2+2ab+b^2\qquad(*)`

`(x+t)^2=x^2+2xt+t^2`

Come back to substitution:

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

Use (*) and the distributive property: a(b + c) = ab + ac

`x^2+2xy+2xz+y^2+2yz+z^2\\\\x^2+y^2+z^2+2xy+2xz+2yz`