Find the Product ((x+1)(x-1))^2

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Move $- 1$ to the left of $x$ .

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

Rewrite $- 1 x$ as $- x$ .

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

Multiply $x$ by $1$ .

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

Multiply $- 1$ by $1$ .

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

Add $- x$ and $x$ .

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

Add $x^{2}$ and $0$ .

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

Step 3

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

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

Step 4

Expand $(x^{2} - 1) (x^{2} - 1)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

$x^{2} x^{2} + x^{2} \cdot - 1 - 1 x^{2} - 1 \cdot - 1$

Step 5

Simplify and combine like terms.

Simplify each term.

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

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

$x^{2 + 2} + x^{2} \cdot - 1 - 1 x^{2} - 1 \cdot - 1$

Add $2$ and $2$ .

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

Move $- 1$ to the left of $x^{2}$ .

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

Rewrite $- 1 x^{2}$ as $- x^{2}$ .

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

Rewrite $- 1 x^{2}$ as $- x^{2}$ .

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

Multiply $- 1$ by $- 1$ .

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

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

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

Find the Product ((x+1)(x-1))^2

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