Algebra Examples

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

Step 1

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

Tap for more steps...

Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify terms.

Tap for more steps...

Step 2.1

Combine the opposite terms in $x \cdot x + x g - g x - g \cdot g$ .

Tap for more steps...

Step 2.1.1

Reorder the factors in the terms $x g$ and $- g x$ .

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

Step 2.1.2

Subtract $g x$ from $g x$ .

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

Step 2.1.3

Add $x \cdot x$ and $0$ .

$(x \cdot x - g \cdot g) (x^{2} - g^{2})$

Step 2.2

Simplify each term.

Tap for more steps...

Step 2.2.1

Multiply $x$ by $x$ .

$(x^{2} - g \cdot g) (x^{2} - g^{2})$

Step 2.2.2

Multiply $g$ by $g$ by adding the exponents.

Tap for more steps...

Step 2.2.2.1

Move $g$ .

$(x^{2} - (g \cdot g)) (x^{2} - g^{2})$

Step 2.2.2.2

Multiply $g$ by $g$ .

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

Step 3

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

Tap for more steps...

Step 3.1

Apply the distributive property.

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

Step 3.2

Apply the distributive property.

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

Step 3.3

Apply the distributive property.

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

Step 4

Simplify and combine like terms.

Tap for more steps...

Step 4.1

Simplify each term.

Tap for more steps...

Step 4.1.1

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

Tap for more steps...

Step 4.1.1.1

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

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

Step 4.1.1.2

Add $2$ and $2$ .

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

Step 4.1.2

Rewrite using the commutative property of multiplication.

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

Step 4.1.3

Rewrite using the commutative property of multiplication.

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

Step 4.1.4

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

Tap for more steps...

Step 4.1.4.1

Move $g^{2}$ .

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

Step 4.1.4.2

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

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

Step 4.1.4.3

Add $2$ and $2$ .

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

Step 4.1.5

Multiply $- 1$ by $- 1$ .

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

Step 4.1.6

Multiply $g^{4}$ by $1$ .

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

Step 4.2

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

Tap for more steps...

Step 4.2.1

Move $x^{2}$ .

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

Step 4.2.2

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

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

Step 5

Move $x^{4}$ .

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

Step 6

Reorder $- 2 g^{2} x^{2}$ and $g^{4}$ .

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