Find the Product (5x^2+2x-3)(x-1)

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

Step 1

Expand $(5 x^{2} + 2 x - 3) (x - 1)$ by multiplying each term in the first expression by each term in the second expression.

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

Step 2

Simplify terms.

Simplify each term.

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Multiply $- 1$ by $5$ .

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $- 1$ by $2$ .

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

Multiply $- 3$ by $- 1$ .

$5 x^{3} - 5 x^{2} + 2 x^{2} - 2 x - 3 x + 3$

Simplify by adding terms.

Add $- 5 x^{2}$ and $2 x^{2}$ .

$5 x^{3} - 3 x^{2} - 2 x - 3 x + 3$

Subtract $3 x$ from $- 2 x$ .

$5 x^{3} - 3 x^{2} - 5 x + 3$