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

The solution to expand (x-2y+z)^2 is x^2+2xz-4xy+4y^2-4yz+z^2

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expand (x-2y+z)^2

expand

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

x^{2} + 2 x z - 4 x y + 4 y^{2} - 4 yz + z^{2}

Solution steps

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

Apply exponent rule:

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

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

= (x - 2 y + z) (x - 2 y + z)

Distribute parentheses

= xx + x (- 2 y) + x z - 2 y x - 2 y (- 2 y) - 2 yz + z x + z (- 2 y) + zz

Simplify

xx + x (- 2 y) + x z - 2 y x - 2 y (- 2 y) - 2 yz + z x + z (- 2 y) + zz : x^{2} + 2 x z - 4 x y + 4 y^{2} - 4 yz + z^{2}

= x^{2} + 2 x z - 4 x y + 4 y^{2} - 4 yz + z^{2}

6 (x + 1)^{2}

\frac{1}{\frac{1}{2}} \cdot 3

15 + (- 2)

\frac{1}{2} n (n + 1)

(5 x^{2} - 3) (x^{2} + x + 4)

What is expand (x-2y+z)^2 ?
The solution to expand (x-2y+z)^2 is x^2+2xz-4xy+4y^2-4yz+z^2