Simplify (2x-1)(4x^2+2x+1)

$(2 x - 1) (4 x^{2} + 2 x + 1)$

Step 1

Expand $(2 x - 1) (4 x^{2} + 2 x + 1)$ by multiplying each term in the first expression by each term in the second expression.

$2 x (4 x^{2}) + 2 x (2 x) + 2 x \cdot 1 - 1 (4 x^{2}) - 1 (2 x) - 1 \cdot 1$

Step 2

Simplify terms.

Combine the opposite terms in $2 x (4 x^{2}) + 2 x (2 x) + 2 x \cdot 1 - 1 (4 x^{2}) - 1 (2 x) - 1 \cdot 1$ .

Reorder the factors in the terms $2 x \cdot 1$ and $- 1 (2 x)$ .

$2 x (4 x^{2}) + 2 x (2 x) + 1 \cdot 2 x - 1 (4 x^{2}) - 1 \cdot 2 x - 1 \cdot 1$

Subtract $2 x$ from $1 \cdot 2 x$ .

$2 x (4 x^{2}) + 2 x (2 x) - 1 (4 x^{2}) + 0 - 1 \cdot 1$

Add $2 x (4 x^{2}) + 2 x (2 x) - 1 (4 x^{2})$ and $0$ .

$2 x (4 x^{2}) + 2 x (2 x) - 1 (4 x^{2}) - 1 \cdot 1$

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 4 x \cdot x^{2} + 2 x (2 x) - 1 (4 x^{2}) - 1 \cdot 1$

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

Move $x^{2}$ .

$2 \cdot 4 (x^{2} x) + 2 x (2 x) - 1 (4 x^{2}) - 1 \cdot 1$

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

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

$2 \cdot 4 (x^{2} x^{1}) + 2 x (2 x) - 1 (4 x^{2}) - 1 \cdot 1$

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

$2 \cdot 4 x^{2 + 1} + 2 x (2 x) - 1 (4 x^{2}) - 1 \cdot 1$

Add $2$ and $1$ .

$2 \cdot 4 x^{3} + 2 x (2 x) - 1 (4 x^{2}) - 1 \cdot 1$

Multiply $2$ by $4$ .

$8 x^{3} + 2 x (2 x) - 1 (4 x^{2}) - 1 \cdot 1$

Rewrite using the commutative property of multiplication.

$8 x^{3} + 2 \cdot 2 x \cdot x - 1 (4 x^{2}) - 1 \cdot 1$

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

Move $x$ .

$8 x^{3} + 2 \cdot 2 (x \cdot x) - 1 (4 x^{2}) - 1 \cdot 1$

Multiply $x$ by $x$ .

$8 x^{3} + 2 \cdot 2 x^{2} - 1 (4 x^{2}) - 1 \cdot 1$

Multiply $2$ by $2$ .

$8 x^{3} + 4 x^{2} - 1 (4 x^{2}) - 1 \cdot 1$

Multiply $4$ by $- 1$ .

$8 x^{3} + 4 x^{2} - 4 x^{2} - 1 \cdot 1$

Multiply $- 1$ by $1$ .

$8 x^{3} + 4 x^{2} - 4 x^{2} - 1$

Combine the opposite terms in $8 x^{3} + 4 x^{2} - 4 x^{2} - 1$ .

Subtract $4 x^{2}$ from $4 x^{2}$ .

$8 x^{3} + 0 - 1$

Add $8 x^{3}$ and $0$ .

$8 x^{3} - 1$

Simplify (2x-1)(4x^2+2x+1)

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