Simplify 3xy^2(2x+y-1)

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

Apply the distributive property.

$3 x y^{2} (2 x) + 3 x y^{2} y + 3 x y^{2} \cdot - 1$

Simplify.

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$3 (x \cdot x) y^{2} \cdot 2 + 3 x y^{2} y + 3 x y^{2} \cdot - 1$

Multiply $x$ by $x$ .

$3 x^{2} y^{2} \cdot 2 + 3 x y^{2} y + 3 x y^{2} \cdot - 1$

Multiply $y^{2}$ by $y$ by adding the exponents.

Move $y$ .

$3 x^{2} y^{2} \cdot 2 + 3 x (y \cdot y^{2}) + 3 x y^{2} \cdot - 1$

Multiply $y$ by $y^{2}$ .

Raise $y$ to the power of $1$ .

$3 x^{2} y^{2} \cdot 2 + 3 x (y^{1} y^{2}) + 3 x y^{2} \cdot - 1$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$3 x^{2} y^{2} \cdot 2 + 3 x y^{1 + 2} + 3 x y^{2} \cdot - 1$

Add $1$ and $2$ .

$3 x^{2} y^{2} \cdot 2 + 3 x y^{3} + 3 x y^{2} \cdot - 1$

Multiply $- 1$ by $3$ .

$3 x^{2} y^{2} \cdot 2 + 3 x y^{3} - 3 x y^{2}$

Multiply $2$ by $3$ .

$6 x^{2} y^{2} + 3 x y^{3} - 3 x y^{2}$