Question

Simplify x(y + z) + x(w + y) + w(x – z).

1. 2xy + xz + xw + wx – wz
2. 2xy + xz + 2xw – wz
3. xy + xz + xw + xy + wx – wz
4. xw + xy + xy + xz + wx – wz

Answer 1

a * (b + c) = a * b + a * c

x(y + z) + x(w + y) + w(x - z) = xy + xz + xw + xy + xw - wz = 2xy + xz + 2xw - wz

Answer: 2.

Answer 2

`\boxed{\boxed{\tt 2)\: 2xy + xz + 2xw - wz}}`

Explanation:

`\tt x(y + z) + x(w + y) + w(x - z)`

Expand by distributing terms:

• 
  `\tt x\left(y+z\right)` →
  `\tt xy+xz`

• 
  `\tt x\left(w+y\right)` →
  `\tt xw+xy`

• 
  `\tt w\left(x-z\right)` →
  `\tt xw-zw`

`\tt xy+xz+xw+xy+xw-zw`

Combine like terms:

`\tt xy+xy+xz+xw+xw-zw`

`\tt (xy+xy)+xz+(wx+wx)-wz`

Simplify:

`\tt 2xy+xz+2wx-wz`

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