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

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

Step 1

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

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

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 $1$ .

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

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

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

Add $1$ and $2$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Move $3$ to the left of $x$ .

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

Multiply $- 2$ by $5$ .

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

Multiply $5$ by $3$ .

$x^{3} - 2 x^{2} + 3 x + 5 x^{2} - 10 x + 15$

Simplify by adding terms.

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

$x^{3} + 3 x^{2} + 3 x - 10 x + 15$

Subtract $10 x$ from $3 x$ .

$x^{3} + 3 x^{2} - 7 x + 15$