What is expand (2x+2y+2z)(2ye^z+2xe^z) ?

The solution to expand (2x+2y+2z)(2ye^z+2xe^z) is 4e^zx^2+8e^zxy+4e^zxz+4e^zy^2+4e^zyz

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expand (2x+2y+2z)(2ye^z+2xe^z)

expand

(2 x + 2 y + 2 z) (2 y e^{z} + 2 x e^{z})

4 e^{z} x^{2} + 8 e^{z} x y + 4 e^{z} x z + 4 e^{z} y^{2} + 4 e^{z} yz

Solution steps

(2 x + 2 y + 2 z) (2 y e^{z} + 2 x e^{z})

= (2 x + 2 y + 2 z) (2 e^{z} y + 2 e^{z} x)

Distribute parentheses

= 2 x \cdot 2 y e^{z} + 2 x \cdot 2 x e^{z} + 2 y \cdot 2 y e^{z} + 2 y \cdot 2 x e^{z} + 2 z \cdot 2 y e^{z} + 2 z \cdot 2 x e^{z}

= 2 \cdot 2 e^{z} x y + 2 \cdot 2 e^{z} xx + 2 \cdot 2 e^{z} yy + 2 \cdot 2 e^{z} x y + 2 \cdot 2 e^{z} yz + 2 \cdot 2 e^{z} x z

Simplify

2 \cdot 2 e^{z} x y + 2 \cdot 2 e^{z} xx + 2 \cdot 2 e^{z} yy + 2 \cdot 2 e^{z} x y + 2 \cdot 2 e^{z} yz + 2 \cdot 2 e^{z} x z : 4 e^{z} x^{2} + 8 e^{z} x y + 4 e^{z} x z + 4 e^{z} y^{2} + 4 e^{z} yz

= 4 e^{z} x^{2} + 8 e^{z} x y + 4 e^{z} x z + 4 e^{z} y^{2} + 4 e^{z} yz

\frac{1}{( a + x ) ( x + b )}

(x + d x) + 5 (x^{2} - 1)

2 e^{3} f (2 e - 3 e f^{2} + f^{3})

(b + d^{2}) a

8 (x + 2)^{2} + y^{2}

What is expand (2x+2y+2z)(2ye^z+2xe^z) ?
The solution to expand (2x+2y+2z)(2ye^z+2xe^z) is 4e^zx^2+8e^zxy+4e^zxz+4e^zy^2+4e^zyz