Expand the Trigonometric Expression (1+x)(x^2-5x-6)

$(1 + x) (x^{2} - 5 x - 6)$

Step 1

Expand $(1 + x) (x^{2} - 5 x - 6)$ by multiplying each term in the first expression by each term in the second expression.

$1 x^{2} + 1 (- 5 x) + 1 \cdot - 6 + x \cdot x^{2} + x (- 5 x) + x \cdot - 6$

Step 2

Simplify terms.

Simplify each term.

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

$x^{2} + 1 (- 5 x) + 1 \cdot - 6 + x \cdot x^{2} + x (- 5 x) + x \cdot - 6$

Multiply $- 5 x$ by $1$ .

$x^{2} - 5 x + 1 \cdot - 6 + x \cdot x^{2} + x (- 5 x) + x \cdot - 6$

Multiply $- 6$ by $1$ .

$x^{2} - 5 x - 6 + x \cdot x^{2} + x (- 5 x) + x \cdot - 6$

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

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

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

$x^{2} - 5 x - 6 + x^{1} x^{2} + x (- 5 x) + x \cdot - 6$

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

$x^{2} - 5 x - 6 + x^{1 + 2} + x (- 5 x) + x \cdot - 6$

Add $1$ and $2$ .

$x^{2} - 5 x - 6 + x^{3} + x (- 5 x) + x \cdot - 6$

Rewrite using the commutative property of multiplication.

$x^{2} - 5 x - 6 + x^{3} - 5 x \cdot x + x \cdot - 6$

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

Move $x$ .

$x^{2} - 5 x - 6 + x^{3} - 5 (x \cdot x) + x \cdot - 6$

Multiply $x$ by $x$ .

$x^{2} - 5 x - 6 + x^{3} - 5 x^{2} + x \cdot - 6$

Move $- 6$ to the left of $x$ .

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

Simplify by adding terms.

Subtract $5 x^{2}$ from $x^{2}$ .

$- 4 x^{2} - 5 x - 6 + x^{3} - 6 x$

Subtract $6 x$ from $- 5 x$ .

$- 4 x^{2} - 11 x - 6 + x^{3}$