Calculus Examples

$lim_{x \to 6} 8 (t - 5) (t - 7)$

Step 1

Evaluate the limit of $8 (t - 5) (t - 7)$ which is constant as $x$ approaches $6$ .

$8 (t - 5) (t - 7)$

Step 2

Simplify the answer.

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Step 2.1

Apply the distributive property.

$(8 t + 8 \cdot - 5) (t - 7)$

Step 2.2

Multiply $8$ by $- 5$ .

$(8 t - 40) (t - 7)$

Step 2.3

Expand $(8 t - 40) (t - 7)$ using the FOIL Method.

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Step 2.3.1

Apply the distributive property.

$8 t (t - 7) - 40 (t - 7)$

Step 2.3.2

Apply the distributive property.

$8 t \cdot t + 8 t \cdot - 7 - 40 (t - 7)$

Step 2.3.3

Apply the distributive property.

$8 t \cdot t + 8 t \cdot - 7 - 40 t - 40 \cdot - 7$

Step 2.4

Simplify and combine like terms.

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Step 2.4.1

Simplify each term.

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Step 2.4.1.1

Multiply $t$ by $t$ by adding the exponents.

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Step 2.4.1.1.1

Move $t$ .

$8 (t \cdot t) + 8 t \cdot - 7 - 40 t - 40 \cdot - 7$

Step 2.4.1.1.2

Multiply $t$ by $t$ .

$8 t^{2} + 8 t \cdot - 7 - 40 t - 40 \cdot - 7$

Step 2.4.1.2

Multiply $- 7$ by $8$ .

$8 t^{2} - 56 t - 40 t - 40 \cdot - 7$

Step 2.4.1.3

Multiply $- 40$ by $- 7$ .

$8 t^{2} - 56 t - 40 t + 280$

Step 2.4.2

Subtract $40 t$ from $- 56 t$ .

$8 t^{2} - 96 t + 280$