Calculus Examples

$2 (10 x^{2} - 24 x) (x - 6) + {(x - 6)}^{2} (20 x - 24)$

Step 1

Factor $x - 6$ out of $2 (10 x^{2} - 24 x) (x - 6) + {(x - 6)}^{2} (20 x - 24)$ .

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Step 1.1

Factor $x - 6$ out of $2 (10 x^{2} - 24 x) (x - 6)$ .

$(x - 6) (2 (10 x^{2} - 24 x)) + {(x - 6)}^{2} (20 x - 24)$

Step 1.2

Factor $x - 6$ out of ${(x - 6)}^{2} (20 x - 24)$ .

$(x - 6) (2 (10 x^{2} - 24 x)) + (x - 6) ((x - 6) (20 x - 24))$

Step 1.3

Factor $x - 6$ out of $(x - 6) (2 (10 x^{2} - 24 x)) + (x - 6) ((x - 6) (20 x - 24))$ .

$(x - 6) (2 (10 x^{2} - 24 x) + (x - 6) (20 x - 24))$

Step 2

Apply the distributive property.

$(x - 6) (2 (10 x^{2}) + 2 (- 24 x) + (x - 6) (20 x - 24))$

Step 3

Multiply $10$ by $2$ .

$(x - 6) (20 x^{2} + 2 (- 24 x) + (x - 6) (20 x - 24))$

Step 4

Multiply $- 24$ by $2$ .

$(x - 6) (20 x^{2} - 48 x + (x - 6) (20 x - 24))$

Step 5

Expand $(x - 6) (20 x - 24)$ using the FOIL Method.

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Step 5.1

Apply the distributive property.

$(x - 6) (20 x^{2} - 48 x + x (20 x - 24) - 6 (20 x - 24))$

Step 5.2

Apply the distributive property.

$(x - 6) (20 x^{2} - 48 x + x (20 x) + x \cdot - 24 - 6 (20 x - 24))$

Step 5.3

Apply the distributive property.

$(x - 6) (20 x^{2} - 48 x + x (20 x) + x \cdot - 24 - 6 (20 x) - 6 \cdot - 24)$

Step 6

Simplify and combine like terms.

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Step 6.1

Simplify each term.

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Step 6.1.1

Rewrite using the commutative property of multiplication.

$(x - 6) (20 x^{2} - 48 x + 20 x \cdot x + x \cdot - 24 - 6 (20 x) - 6 \cdot - 24)$

Step 6.1.2

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

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Step 6.1.2.1

Move $x$ .

$(x - 6) (20 x^{2} - 48 x + 20 (x \cdot x) + x \cdot - 24 - 6 (20 x) - 6 \cdot - 24)$

Step 6.1.2.2

Multiply $x$ by $x$ .

$(x - 6) (20 x^{2} - 48 x + 20 x^{2} + x \cdot - 24 - 6 (20 x) - 6 \cdot - 24)$

Step 6.1.3

Move $- 24$ to the left of $x$ .

$(x - 6) (20 x^{2} - 48 x + 20 x^{2} - 24 x - 6 (20 x) - 6 \cdot - 24)$

Step 6.1.4

Multiply $20$ by $- 6$ .

$(x - 6) (20 x^{2} - 48 x + 20 x^{2} - 24 x - 120 x - 6 \cdot - 24)$

Step 6.1.5

Multiply $- 6$ by $- 24$ .

$(x - 6) (20 x^{2} - 48 x + 20 x^{2} - 24 x - 120 x + 144)$

Step 6.2

Subtract $120 x$ from $- 24 x$ .

$(x - 6) (20 x^{2} - 48 x + 20 x^{2} - 144 x + 144)$

Step 7

Add $20 x^{2}$ and $20 x^{2}$ .

$(x - 6) (40 x^{2} - 48 x - 144 x + 144)$

Step 8

Subtract $144 x$ from $- 48 x$ .

$(x - 6) (40 x^{2} - 192 x + 144)$

Step 9

Factor.

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Step 9.1

Factor $8$ out of $40 x^{2} - 192 x + 144$ .

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Step 9.1.1

Factor $8$ out of $40 x^{2}$ .

$(x - 6) (8 (5 x^{2}) - 192 x + 144)$

Step 9.1.2

Factor $8$ out of $- 192 x$ .

$(x - 6) (8 (5 x^{2}) + 8 (- 24 x) + 144)$

Step 9.1.3

Factor $8$ out of $144$ .

$(x - 6) (8 (5 x^{2}) + 8 (- 24 x) + 8 (18))$

Step 9.1.4

Factor $8$ out of $8 (5 x^{2}) + 8 (- 24 x)$ .

$(x - 6) (8 (5 x^{2} - 24 x) + 8 (18))$

Step 9.1.5

Factor $8$ out of $8 (5 x^{2} - 24 x) + 8 (18)$ .

$(x - 6) (8 (5 x^{2} - 24 x + 18))$

Step 9.2

Remove unnecessary parentheses.

$(x - 6) \cdot 8 (5 x^{2} - 24 x + 18)$