Simplify (2y^2)(4xy^3)+(3xy^4)(5y)

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

Step 1

Simplify each term.

Multiply $y^{2}$ by $y^{3}$ by adding the exponents.

Move $y^{3}$ .

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

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

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

Add $3$ and $2$ .

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

Rewrite using the commutative property of multiplication.

$2 \cdot 4 y^{5} x + (3 x y^{4}) (5 y)$

Multiply $2$ by $4$ .

$8 y^{5} x + (3 x y^{4}) (5 y)$

Multiply $y^{4}$ by $y$ by adding the exponents.

Move $y$ .

$8 y^{5} x + 3 x (y \cdot y^{4}) \cdot 5$

Multiply $y$ by $y^{4}$ .

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

$8 y^{5} x + 3 x (y^{1} y^{4}) \cdot 5$

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

$8 y^{5} x + 3 x y^{1 + 4} \cdot 5$

Add $1$ and $4$ .

$8 y^{5} x + 3 x y^{5} \cdot 5$

Multiply $5$ by $3$ .

$8 y^{5} x + 15 x y^{5}$

Step 2

Add $8 y^{5} x$ and $15 x y^{5}$ .

Move $y^{5}$ .

$8 x y^{5} + 15 x y^{5}$

Add $8 x y^{5}$ and $15 x y^{5}$ .

$23 x y^{5}$