Calculus Examples

${(x^{2} - 3)}^{2}$

Step 1

Rewrite ${(x^{2} - 3)}^{2}$ as $(x^{2} - 3) (x^{2} - 3)$ .

$(x^{2} - 3) (x^{2} - 3)$

Step 2

Expand $(x^{2} - 3) (x^{2} - 3)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$x^{2} (x^{2} - 3) - 3 (x^{2} - 3)$

Step 2.2

Apply the distributive property.

$x^{2} x^{2} + x^{2} \cdot - 3 - 3 (x^{2} - 3)$

Step 2.3

Apply the distributive property.

$x^{2} x^{2} + x^{2} \cdot - 3 - 3 x^{2} - 3 \cdot - 3$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

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

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Step 3.1.1.1

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

$x^{2 + 2} + x^{2} \cdot - 3 - 3 x^{2} - 3 \cdot - 3$

Step 3.1.1.2

Add $2$ and $2$ .

$x^{4} + x^{2} \cdot - 3 - 3 x^{2} - 3 \cdot - 3$

Step 3.1.2

Move $- 3$ to the left of $x^{2}$ .

$x^{4} - 3 \cdot x^{2} - 3 x^{2} - 3 \cdot - 3$

Step 3.1.3

Multiply $- 3$ by $- 3$ .

$x^{4} - 3 x^{2} - 3 x^{2} + 9$

Step 3.2

Subtract $3 x^{2}$ from $- 3 x^{2}$ .

$x^{4} - 6 x^{2} + 9$