Calculus Examples

${(6 x - 3)}^{2} - 9$

Step 1

Simplify each term.

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Step 1.1

Rewrite ${(6 x - 3)}^{2}$ as $(6 x - 3) (6 x - 3)$ .

$(6 x - 3) (6 x - 3) - 9$

Step 1.2

Expand $(6 x - 3) (6 x - 3)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$6 x (6 x - 3) - 3 (6 x - 3) - 9$

Step 1.2.2

Apply the distributive property.

$6 x (6 x) + 6 x \cdot - 3 - 3 (6 x - 3) - 9$

Step 1.2.3

Apply the distributive property.

$6 x (6 x) + 6 x \cdot - 3 - 3 (6 x) - 3 \cdot - 3 - 9$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Rewrite using the commutative property of multiplication.

$6 \cdot 6 x \cdot x + 6 x \cdot - 3 - 3 (6 x) - 3 \cdot - 3 - 9$

Step 1.3.1.2

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

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Step 1.3.1.2.1

Move $x$ .

$6 \cdot 6 (x \cdot x) + 6 x \cdot - 3 - 3 (6 x) - 3 \cdot - 3 - 9$

Step 1.3.1.2.2

Multiply $x$ by $x$ .

$6 \cdot 6 x^{2} + 6 x \cdot - 3 - 3 (6 x) - 3 \cdot - 3 - 9$

Step 1.3.1.3

Multiply $6$ by $6$ .

$36 x^{2} + 6 x \cdot - 3 - 3 (6 x) - 3 \cdot - 3 - 9$

Step 1.3.1.4

Multiply $- 3$ by $6$ .

$36 x^{2} - 18 x - 3 (6 x) - 3 \cdot - 3 - 9$

Step 1.3.1.5

Multiply $6$ by $- 3$ .

$36 x^{2} - 18 x - 18 x - 3 \cdot - 3 - 9$

Step 1.3.1.6

Multiply $- 3$ by $- 3$ .

$36 x^{2} - 18 x - 18 x + 9 - 9$

Step 1.3.2

Subtract $18 x$ from $- 18 x$ .

$36 x^{2} - 36 x + 9 - 9$

Step 2

Combine the opposite terms in $36 x^{2} - 36 x + 9 - 9$ .

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Step 2.1

Subtract $9$ from $9$ .

$36 x^{2} - 36 x + 0$

Step 2.2

Add $36 x^{2} - 36 x$ and $0$ .

$36 x^{2} - 36 x$