Simplify (x+5)(x^2-3x+1)

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

Step 1

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

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

Step 2

Simplify terms.

Simplify each term.

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

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

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

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

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

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

Add $1$ and $2$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $x$ by $1$ .

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

Multiply $- 3$ by $5$ .

$x^{3} - 3 x^{2} + x + 5 x^{2} - 15 x + 5 \cdot 1$

Multiply $5$ by $1$ .

$x^{3} - 3 x^{2} + x + 5 x^{2} - 15 x + 5$

Simplify by adding terms.

Add $- 3 x^{2}$ and $5 x^{2}$ .

$x^{3} + 2 x^{2} + x - 15 x + 5$

Subtract $15 x$ from $x$ .

$x^{3} + 2 x^{2} - 14 x + 5$