Find the Product (2a-1)(1+2a)

$(2 a - 1) (1 + 2 a)$

Expand $(2 a - 1) (1 + 2 a)$ using the FOIL Method.

Apply the distributive property.

$2 a (1 + 2 a) - 1 (1 + 2 a)$

Apply the distributive property.

$2 a \cdot 1 + 2 a (2 a) - 1 (1 + 2 a)$

Apply the distributive property.

$2 a \cdot 1 + 2 a (2 a) - 1 \cdot 1 - 1 (2 a)$

Simplify terms.

Combine the opposite terms in $2 a \cdot 1 + 2 a (2 a) - 1 \cdot 1 - 1 (2 a)$ .

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

$1 \cdot 2 a + 2 a (2 a) - 1 \cdot 1 - 1 \cdot 2 a$

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

$0 + 2 a (2 a) - 1 \cdot 1$

Add $0$ and $2 a (2 a)$ .

$2 a (2 a) - 1 \cdot 1$

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 2 a \cdot a - 1 \cdot 1$

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

$2 \cdot 2 (a \cdot a) - 1 \cdot 1$

Multiply $a$ by $a$ .

$2 \cdot 2 a^{2} - 1 \cdot 1$

Multiply $2$ by $2$ .

$4 a^{2} - 1 \cdot 1$

Multiply $- 1$ by $1$ .

$4 a^{2} - 1$