What is expand (2x+3y+4z)^2 ?

The solution to expand (2x+3y+4z)^2 is 4x^2+12xy+16xz+9y^2+24yz+16z^2

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expand (2x+3y+4z)^2

expand

(2 x + 3 y + 4 z)^{2}

4 x^{2} + 12 x y + 16 x z + 9 y^{2} + 24 yz + 16 z^{2}

Solution steps

(2 x + 3 y + 4 z)^{2}

Apply exponent rule:

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

(2 x + 3 y + 4 z)^{2} = (2 x + 3 y + 4 z) (2 x + 3 y + 4 z)

= (2 x + 3 y + 4 z) (2 x + 3 y + 4 z)

Distribute parentheses

= 2 x \cdot 2 x + 2 x \cdot 3 y + 2 x \cdot 4 z + 3 y \cdot 2 x + 3 y \cdot 3 y + 3 y \cdot 4 z + 4 z \cdot 2 x + 4 z \cdot 3 y + 4 z \cdot 4 z

Simplify

2 x \cdot 2 x + 2 x \cdot 3 y + 2 x \cdot 4 z + 3 y \cdot 2 x + 3 y \cdot 3 y + 3 y \cdot 4 z + 4 z \cdot 2 x + 4 z \cdot 3 y + 4 z \cdot 4 z : 4 x^{2} + 12 x y + 16 x z + 9 y^{2} + 24 yz + 16 z^{2}

= 4 x^{2} + 12 x y + 16 x z + 9 y^{2} + 24 yz + 16 z^{2}

t^{4} (n)

(x^{2} + 1) (x^{2} - 2 x^{a} - 2 x^{a} + 2 - x^{2} + 2009)

(81 x^{- 2} 4 y^{16} z^{52})^{0} + 7

5 a^{2} - 20 b^{2}

(2 x + 3 y)^{3} + 2 (2 x + 3 y) + 1

What is expand (2x+3y+4z)^2 ?
The solution to expand (2x+3y+4z)^2 is 4x^2+12xy+16xz+9y^2+24yz+16z^2