Simplify (4x-1)^2

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

Step 1

Rewrite ${(4 x - 1)}^{2}$ as $(4 x - 1) (4 x - 1)$ .

$(4 x - 1) (4 x - 1)$

Step 2

Expand $(4 x - 1) (4 x - 1)$ using the FOIL Method.

Apply the distributive property.

$4 x (4 x - 1) - 1 (4 x - 1)$

Apply the distributive property.

$4 x (4 x) + 4 x \cdot - 1 - 1 (4 x - 1)$

Apply the distributive property.

$4 x (4 x) + 4 x \cdot - 1 - 1 (4 x) - 1 \cdot - 1$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$4 \cdot 4 x \cdot x + 4 x \cdot - 1 - 1 (4 x) - 1 \cdot - 1$

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

Move $x$ .

$4 \cdot 4 (x \cdot x) + 4 x \cdot - 1 - 1 (4 x) - 1 \cdot - 1$

Multiply $x$ by $x$ .

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

Multiply $4$ by $4$ .

$16 x^{2} + 4 x \cdot - 1 - 1 (4 x) - 1 \cdot - 1$

Multiply $- 1$ by $4$ .

$16 x^{2} - 4 x - 1 (4 x) - 1 \cdot - 1$

Multiply $4$ by $- 1$ .

$16 x^{2} - 4 x - 4 x - 1 \cdot - 1$

Multiply $- 1$ by $- 1$ .

$16 x^{2} - 4 x - 4 x + 1$

Subtract $4 x$ from $- 4 x$ .

$16 x^{2} - 8 x + 1$