What is expand (x+xy+y)^2 ?

The solution to expand (x+xy+y)^2 is x^2+2x^2y+2xy+x^2y^2+2xy^2+y^2

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expand (x+xy+y)^2

expand

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

x^{2} + 2 x^{2} y + 2 x y + x^{2} y^{2} + 2 x y^{2} + y^{2}

Solution steps

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

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

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

= (x + x y + y) (x + x y + y)

Distribute parentheses

= xx + xx y + x y + x y x + x y x y + x yy + y x + y x y + yy

Simplify

xx + xx y + x y + x y x + x y x y + x yy + y x + y x y + yy : x^{2} + 2 x^{2} y + 2 x y + x^{2} y^{2} + 2 x y^{2} + y^{2}

= x^{2} + 2 x^{2} y + 2 x y + x^{2} y^{2} + 2 x y^{2} + y^{2}

- pq + 3 q^{2} - 4 pq - q^{2} + 8 p^{3} - 2 q

(10 x^{2} + 3) - (9 x^{2} + 4 x + 1)

\frac{x + 1}{x - 1} + \frac{1}{x}

4 (3 - 4 x)

What is expand (x+xy+y)^2 ?
The solution to expand (x+xy+y)^2 is x^2+2x^2y+2xy+x^2y^2+2xy^2+y^2