Simplify (-6x-1)(36x^2-6x+1)

$(- 6 x - 1) (36 x^{2} - 6 x + 1)$

Step 1

Expand $(- 6 x - 1) (36 x^{2} - 6 x + 1)$ by multiplying each term in the first expression by each term in the second expression.

$- 6 x (36 x^{2}) - 6 x (- 6 x) - 6 x \cdot 1 - 1 (36 x^{2}) - 1 (- 6 x) - 1 \cdot 1$

Step 2

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$- 6 \cdot 36 x \cdot x^{2} - 6 x (- 6 x) - 6 x \cdot 1 - 1 (36 x^{2}) - 1 (- 6 x) - 1 \cdot 1$

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

Move $x^{2}$ .

$- 6 \cdot 36 (x^{2} x) - 6 x (- 6 x) - 6 x \cdot 1 - 1 (36 x^{2}) - 1 (- 6 x) - 1 \cdot 1$

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

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

$- 6 \cdot 36 (x^{2} x^{1}) - 6 x (- 6 x) - 6 x \cdot 1 - 1 (36 x^{2}) - 1 (- 6 x) - 1 \cdot 1$

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

$- 6 \cdot 36 x^{2 + 1} - 6 x (- 6 x) - 6 x \cdot 1 - 1 (36 x^{2}) - 1 (- 6 x) - 1 \cdot 1$

Add $2$ and $1$ .

$- 6 \cdot 36 x^{3} - 6 x (- 6 x) - 6 x \cdot 1 - 1 (36 x^{2}) - 1 (- 6 x) - 1 \cdot 1$

Multiply $- 6$ by $36$ .

$- 216 x^{3} - 6 x (- 6 x) - 6 x \cdot 1 - 1 (36 x^{2}) - 1 (- 6 x) - 1 \cdot 1$

Rewrite using the commutative property of multiplication.

$- 216 x^{3} - 6 \cdot - 6 x \cdot x - 6 x \cdot 1 - 1 (36 x^{2}) - 1 (- 6 x) - 1 \cdot 1$

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

Move $x$ .

$- 216 x^{3} - 6 \cdot - 6 (x \cdot x) - 6 x \cdot 1 - 1 (36 x^{2}) - 1 (- 6 x) - 1 \cdot 1$

Multiply $x$ by $x$ .

$- 216 x^{3} - 6 \cdot - 6 x^{2} - 6 x \cdot 1 - 1 (36 x^{2}) - 1 (- 6 x) - 1 \cdot 1$

Multiply $- 6$ by $- 6$ .

$- 216 x^{3} + 36 x^{2} - 6 x \cdot 1 - 1 (36 x^{2}) - 1 (- 6 x) - 1 \cdot 1$

Multiply $- 6$ by $1$ .

$- 216 x^{3} + 36 x^{2} - 6 x - 1 (36 x^{2}) - 1 (- 6 x) - 1 \cdot 1$

Multiply $36$ by $- 1$ .

$- 216 x^{3} + 36 x^{2} - 6 x - 36 x^{2} - 1 (- 6 x) - 1 \cdot 1$

Multiply $- 6$ by $- 1$ .

$- 216 x^{3} + 36 x^{2} - 6 x - 36 x^{2} + 6 x - 1 \cdot 1$

Multiply $- 1$ by $1$ .

$- 216 x^{3} + 36 x^{2} - 6 x - 36 x^{2} + 6 x - 1$

Combine the opposite terms in $- 216 x^{3} + 36 x^{2} - 6 x - 36 x^{2} + 6 x - 1$ .

Subtract $36 x^{2}$ from $36 x^{2}$ .

$- 216 x^{3} - 6 x + 0 + 6 x - 1$

Add $- 216 x^{3} - 6 x$ and $0$ .

$- 216 x^{3} - 6 x + 6 x - 1$

Add $- 6 x$ and $6 x$ .

$- 216 x^{3} + 0 - 1$

Add $- 216 x^{3}$ and $0$ .

$- 216 x^{3} - 1$

Simplify (-6x-1)(36x^2-6x+1)

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