What is expand (3x+4y+5z)^2 ?

The solution to expand (3x+4y+5z)^2 is 9x^2+24xy+30xz+16y^2+40yz+25z^2

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expand (3x+4y+5z)^2

expand

(3 x + 4 y + 5 z)^{2}

9 x^{2} + 24 x y + 30 x z + 16 y^{2} + 40 yz + 25 z^{2}

Solution steps

(3 x + 4 y + 5 z)^{2}

Apply exponent rule:

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

(3 x + 4 y + 5 z)^{2} = (3 x + 4 y + 5 z) (3 x + 4 y + 5 z)

= (3 x + 4 y + 5 z) (3 x + 4 y + 5 z)

Distribute parentheses

= 3 x \cdot 3 x + 3 x \cdot 4 y + 3 x \cdot 5 z + 4 y \cdot 3 x + 4 y \cdot 4 y + 4 y \cdot 5 z + 5 z \cdot 3 x + 5 z \cdot 4 y + 5 z \cdot 5 z

Simplify

3 x \cdot 3 x + 3 x \cdot 4 y + 3 x \cdot 5 z + 4 y \cdot 3 x + 4 y \cdot 4 y + 4 y \cdot 5 z + 5 z \cdot 3 x + 5 z \cdot 4 y + 5 z \cdot 5 z : 9 x^{2} + 24 x y + 30 x z + 16 y^{2} + 40 yz + 25 z^{2}

= 9 x^{2} + 24 x y + 30 x z + 16 y^{2} + 40 yz + 25 z^{2}

\frac{a ^{2} - 25}{a - 5}

48 a^{4} + 108 a^{2} b^{2} + 243 b^{2}

- \frac{2}{( x - 1 )} + 1 - \frac{( x + 1 )}{( x + 2 )}

20 x^{2} - 45 y^{2}

\frac{( \frac{( m + 1 )}{2} - \frac{( m - 1 )}{3} )}{( \frac{( m + 1 )}{5} )}

What is expand (3x+4y+5z)^2 ?
The solution to expand (3x+4y+5z)^2 is 9x^2+24xy+30xz+16y^2+40yz+25z^2