Simplify (5x+2y)(x^2-3xy+6)

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

Expand $(5 x + 2 y) (x^{2} - 3 x y + 6)$ by multiplying each term in the first expression by each term in the second expression.

$5 x \cdot x^{2} + 5 x (- 3 x y) + 5 x \cdot 6 + 2 y x^{2} + 2 y (- 3 x y) + 2 y \cdot 6$

Simplify each term.

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

Move $x^{2}$ .

$5 (x^{2} x) + 5 x (- 3 x y) + 5 x \cdot 6 + 2 y x^{2} + 2 y (- 3 x y) + 2 y \cdot 6$

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

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

$5 (x^{2} x^{1}) + 5 x (- 3 x y) + 5 x \cdot 6 + 2 y x^{2} + 2 y (- 3 x y) + 2 y \cdot 6$

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

$5 x^{2 + 1} + 5 x (- 3 x y) + 5 x \cdot 6 + 2 y x^{2} + 2 y (- 3 x y) + 2 y \cdot 6$

Add $2$ and $1$ .

$5 x^{3} + 5 x (- 3 x y) + 5 x \cdot 6 + 2 y x^{2} + 2 y (- 3 x y) + 2 y \cdot 6$

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

Move $x$ .

$5 x^{3} + 5 (x \cdot x) (- 3 y) + 5 x \cdot 6 + 2 y x^{2} + 2 y (- 3 x y) + 2 y \cdot 6$

Multiply $x$ by $x$ .

$5 x^{3} + 5 x^{2} (- 3 y) + 5 x \cdot 6 + 2 y x^{2} + 2 y (- 3 x y) + 2 y \cdot 6$

Rewrite using the commutative property of multiplication.

$5 x^{3} + 5 \cdot - 3 x^{2} y + 5 x \cdot 6 + 2 y x^{2} + 2 y (- 3 x y) + 2 y \cdot 6$

Multiply $5$ by $- 3$ .

$5 x^{3} - 15 x^{2} y + 5 x \cdot 6 + 2 y x^{2} + 2 y (- 3 x y) + 2 y \cdot 6$

Multiply $6$ by $5$ .

$5 x^{3} - 15 x^{2} y + 30 x + 2 y x^{2} + 2 y (- 3 x y) + 2 y \cdot 6$

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$5 x^{3} - 15 x^{2} y + 30 x + 2 y x^{2} + 2 (y \cdot y) (- 3 x) + 2 y \cdot 6$

Multiply $y$ by $y$ .

$5 x^{3} - 15 x^{2} y + 30 x + 2 y x^{2} + 2 y^{2} (- 3 x) + 2 y \cdot 6$

Rewrite using the commutative property of multiplication.

$5 x^{3} - 15 x^{2} y + 30 x + 2 y x^{2} + 2 \cdot - 3 y^{2} x + 2 y \cdot 6$

Multiply $2$ by $- 3$ .

$5 x^{3} - 15 x^{2} y + 30 x + 2 y x^{2} - 6 y^{2} x + 2 y \cdot 6$

Multiply $6$ by $2$ .

$5 x^{3} - 15 x^{2} y + 30 x + 2 y x^{2} - 6 y^{2} x + 12 y$

Add $- 15 x^{2} y$ and $2 y x^{2}$ .

Move $y$ .

$5 x^{3} - 15 x^{2} y + 2 x^{2} y + 30 x - 6 y^{2} x + 12 y$

Add $- 15 x^{2} y$ and $2 x^{2} y$ .

$5 x^{3} - 13 x^{2} y + 30 x - 6 y^{2} x + 12 y$

Move $y^{2}$ .

$5 x^{3} - 13 x^{2} y + 30 x - 6 x y^{2} + 12 y$

Move $30 x$ .

$5 x^{3} - 13 x^{2} y - 6 x y^{2} + 12 y + 30 x$

Move $5 x^{3}$ .

$- 13 x^{2} y - 6 x y^{2} + 5 x^{3} + 12 y + 30 x$

Reorder $- 13 x^{2} y$ and $- 6 x y^{2}$ .

$- 6 x y^{2} - 13 x^{2} y + 5 x^{3} + 12 y + 30 x$

Simplify (5x+2y)(x^2-3xy+6)

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