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

Answer:

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

Step-by-step 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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