Find the Product (4x^2+x-5)(2x+1)

$(4 x^{2} + x - 5) (2 x + 1)$

Expand $(4 x^{2} + x - 5) (2 x + 1)$ by multiplying each term in the first expression by each term in the second expression.

$4 x^{2} (2 x) + 4 x^{2} \cdot 1 + x (2 x) + x \cdot 1 - 5 (2 x) - 5 \cdot 1$

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$4 \cdot 2 x^{2} x + 4 x^{2} \cdot 1 + x (2 x) + x \cdot 1 - 5 (2 x) - 5 \cdot 1$

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

Move $x$ .

$4 \cdot 2 (x \cdot x^{2}) + 4 x^{2} \cdot 1 + x (2 x) + x \cdot 1 - 5 (2 x) - 5 \cdot 1$

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

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

$4 \cdot 2 (x^{1} x^{2}) + 4 x^{2} \cdot 1 + x (2 x) + x \cdot 1 - 5 (2 x) - 5 \cdot 1$

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

$4 \cdot 2 x^{1 + 2} + 4 x^{2} \cdot 1 + x (2 x) + x \cdot 1 - 5 (2 x) - 5 \cdot 1$

Add $1$ and $2$ .

$4 \cdot 2 x^{3} + 4 x^{2} \cdot 1 + x (2 x) + x \cdot 1 - 5 (2 x) - 5 \cdot 1$

Multiply $4$ by $2$ .

$8 x^{3} + 4 x^{2} \cdot 1 + x (2 x) + x \cdot 1 - 5 (2 x) - 5 \cdot 1$

Multiply $4$ by $1$ .

$8 x^{3} + 4 x^{2} + x (2 x) + x \cdot 1 - 5 (2 x) - 5 \cdot 1$

Rewrite using the commutative property of multiplication.

$8 x^{3} + 4 x^{2} + 2 x \cdot x + x \cdot 1 - 5 (2 x) - 5 \cdot 1$

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

Move $x$ .

$8 x^{3} + 4 x^{2} + 2 (x \cdot x) + x \cdot 1 - 5 (2 x) - 5 \cdot 1$

Multiply $x$ by $x$ .

$8 x^{3} + 4 x^{2} + 2 x^{2} + x \cdot 1 - 5 (2 x) - 5 \cdot 1$

Multiply $x$ by $1$ .

$8 x^{3} + 4 x^{2} + 2 x^{2} + x - 5 (2 x) - 5 \cdot 1$

Multiply $2$ by $- 5$ .

$8 x^{3} + 4 x^{2} + 2 x^{2} + x - 10 x - 5 \cdot 1$

Multiply $- 5$ by $1$ .

$8 x^{3} + 4 x^{2} + 2 x^{2} + x - 10 x - 5$

Simplify by adding terms.

Add $4 x^{2}$ and $2 x^{2}$ .

$8 x^{3} + 6 x^{2} + x - 10 x - 5$

Subtract $10 x$ from $x$ .

$8 x^{3} + 6 x^{2} - 9 x - 5$