What is expand (2x-3y+5z)^2 ?

The solution to expand (2x-3y+5z)^2 is 4x^2-12xy+20xz+9y^2-30yz+25z^2

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expand (2x-3y+5z)^2

expand

(2 x - 3 y + 5 z)^{2}

4 x^{2} - 12 x y + 20 x z + 9 y^{2} - 30 yz + 25 z^{2}

Solution steps

(2 x - 3 y + 5 z)^{2}

Apply exponent rule:

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

(2 x - 3 y + 5 z)^{2} = (2 x - 3 y + 5 z) (2 x - 3 y + 5 z)

= (2 x - 3 y + 5 z) (2 x - 3 y + 5 z)

Distribute parentheses

= 2 x \cdot 2 x + 2 x (- 3 y) + 2 x \cdot 5 z - 3 y \cdot 2 x - 3 y (- 3 y) - 3 y \cdot 5 z + 5 z \cdot 2 x + 5 z (- 3 y) + 5 z \cdot 5 z

Simplify

2 x \cdot 2 x + 2 x (- 3 y) + 2 x \cdot 5 z - 3 y \cdot 2 x - 3 y (- 3 y) - 3 y \cdot 5 z + 5 z \cdot 2 x + 5 z (- 3 y) + 5 z \cdot 5 z : 4 x^{2} - 12 x y + 20 x z + 9 y^{2} - 30 yz + 25 z^{2}

= 4 x^{2} - 12 x y + 20 x z + 9 y^{2} - 30 yz + 25 z^{2}

14 - (- 3^{2})

4 (x^{2} - 6) - 3 x (x + 5)

\frac{- x + 7}{3 x ^{3} - 21 x ^{2}}

\frac{65}{12}

y^{- \frac{3}{2}} \cdot y^{- 1}

What is expand (2x-3y+5z)^2 ?
The solution to expand (2x-3y+5z)^2 is 4x^2-12xy+20xz+9y^2-30yz+25z^2