Simplify (4ax-1)^2

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

Step 1

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

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

Step 2

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

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

Move $a$ .

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

Multiply $a$ by $a$ .

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $4$ by $4$ .

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

Multiply $- 1$ by $4$ .

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

Multiply $4$ by $- 1$ .

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

Multiply $- 1$ by $- 1$ .

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

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

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