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

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

Step 1

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

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

Step 2

Simplify terms.

Combine the opposite terms in $x^{2} x + x^{2} \cdot 1 + x \cdot x + x \cdot 1 - 1 x - 1 \cdot 1$ .

Reorder the factors in the terms $x \cdot 1$ and $- 1 x$ .

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

Subtract $1 x$ from $1 x$ .

$x^{2} x + x^{2} \cdot 1 + x \cdot x + 0 - 1 \cdot 1$

Add $x^{2} x + x^{2} \cdot 1 + x \cdot x$ and $0$ .

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

Simplify each term.

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

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

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

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

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

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

Add $2$ and $1$ .

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

Multiply $x^{2}$ by $1$ .

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

Multiply $x$ by $x$ .

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

Multiply $- 1$ by $1$ .

$x^{3} + x^{2} + x^{2} - 1$

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

$x^{3} + 2 x^{2} - 1$