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

The solution to expand (5x+3/2 y+z)^2 is (100x^2+9y^2+4z^2)/4+15xy+10xz+3yz

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

expand

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

\frac{100 x ^{2} + 9 y ^{2} + 4 z ^{2}}{4} + 15 x y + 10 x z + 3 yz

Solution steps

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

Apply exponent rule:

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

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

= (5 x + \frac{3}{2} y + z) (5 x + \frac{3}{2} y + z)

Distribute parentheses

= 5 x \cdot 5 x + 5 x \frac{3}{2} y + 5 x z + \frac{3}{2} y \cdot 5 x + \frac{3}{2} y \frac{3}{2} y + \frac{3}{2} yz + z \cdot 5 x + z \frac{3}{2} y + zz

Simplify

5 x \cdot 5 x + 5 x \frac{3}{2} y + 5 x z + \frac{3}{2} y \cdot 5 x + \frac{3}{2} y \frac{3}{2} y + \frac{3}{2} yz + z \cdot 5 x + z \frac{3}{2} y + zz : \frac{100 x ^{2} + 9 y ^{2} + 4 z ^{2}}{4} + 15 x y + 10 x z + 3 yz

= \frac{100 x ^{2} + 9 y ^{2} + 4 z ^{2}}{4} + 15 x y + 10 x z + 3 yz

(x^{2} - x sec^{2} (y)) d y

- \frac{e ^{4 x} ( 2 e ^{- 2 x} - e ^{- x} )}{6}

(8 t^{7}, 5 t^{3}, - 4 t^{3}) l e f t (1, 2 t, 3 t^{2})

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

(1 + x) d x

What is expand (5x+3/2 y+z)^2 ?
The solution to expand (5x+3/2 y+z)^2 is (100x^2+9y^2+4z^2)/4+15xy+10xz+3yz