Find the Product xy(5x^2+8x-7)

$x y (5 x^{2} + 8 x - 7)$

Step 1

Apply the distributive property.

$x y (5 x^{2}) + x y (8 x) + x y \cdot - 7$

Step 2

Simplify.

Rewrite using the commutative property of multiplication.

$5 x y x^{2} + x y (8 x) + x y \cdot - 7$

Rewrite using the commutative property of multiplication.

$5 x y x^{2} + 8 x y x + x y \cdot - 7$

Move $- 7$ to the left of $x y$ .

$5 x y x^{2} + 8 x y x - 7 \cdot (x y)$

Step 3

Simplify each term.

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

Move $x^{2}$ .

$5 (x^{2} x) y + 8 x y x - 7 \cdot (x y)$

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

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

$5 (x^{2} x^{1}) y + 8 x y x - 7 \cdot (x y)$

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

$5 x^{2 + 1} y + 8 x y x - 7 \cdot (x y)$

Add $2$ and $1$ .

$5 x^{3} y + 8 x y x - 7 \cdot (x y)$

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

Move $x$ .

$5 x^{3} y + 8 (x \cdot x) y - 7 \cdot (x y)$

Multiply $x$ by $x$ .

$5 x^{3} y + 8 x^{2} y - 7 \cdot (x y)$

$5 x^{3} y + 8 x^{2} y - 7 x y$