Finite Math Examples

$(2 t^{4} - 5 t^{3}) (7 t^{3} - 4 t^{2})$

Step 1

Expand $(2 t^{4} - 5 t^{3}) (7 t^{3} - 4 t^{2})$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$2 t^{4} (7 t^{3} - 4 t^{2}) - 5 t^{3} (7 t^{3} - 4 t^{2})$

Step 1.2

Apply the distributive property.

$2 t^{4} (7 t^{3}) + 2 t^{4} (- 4 t^{2}) - 5 t^{3} (7 t^{3} - 4 t^{2})$

Step 1.3

Apply the distributive property.

$2 t^{4} (7 t^{3}) + 2 t^{4} (- 4 t^{2}) - 5 t^{3} (7 t^{3}) - 5 t^{3} (- 4 t^{2})$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite using the commutative property of multiplication.

$2 \cdot 7 t^{4} t^{3} + 2 t^{4} (- 4 t^{2}) - 5 t^{3} (7 t^{3}) - 5 t^{3} (- 4 t^{2})$

Step 2.1.2

Multiply $t^{4}$ by $t^{3}$ by adding the exponents.

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Step 2.1.2.1

Move $t^{3}$ .

$2 \cdot 7 (t^{3} t^{4}) + 2 t^{4} (- 4 t^{2}) - 5 t^{3} (7 t^{3}) - 5 t^{3} (- 4 t^{2})$

Step 2.1.2.2

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

$2 \cdot 7 t^{3 + 4} + 2 t^{4} (- 4 t^{2}) - 5 t^{3} (7 t^{3}) - 5 t^{3} (- 4 t^{2})$

Step 2.1.2.3

Add $3$ and $4$ .

$2 \cdot 7 t^{7} + 2 t^{4} (- 4 t^{2}) - 5 t^{3} (7 t^{3}) - 5 t^{3} (- 4 t^{2})$

Step 2.1.3

Multiply $2$ by $7$ .

$14 t^{7} + 2 t^{4} (- 4 t^{2}) - 5 t^{3} (7 t^{3}) - 5 t^{3} (- 4 t^{2})$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$14 t^{7} + 2 \cdot - 4 t^{4} t^{2} - 5 t^{3} (7 t^{3}) - 5 t^{3} (- 4 t^{2})$

Step 2.1.5

Multiply $t^{4}$ by $t^{2}$ by adding the exponents.

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Step 2.1.5.1

Move $t^{2}$ .

$14 t^{7} + 2 \cdot - 4 (t^{2} t^{4}) - 5 t^{3} (7 t^{3}) - 5 t^{3} (- 4 t^{2})$

Step 2.1.5.2

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

$14 t^{7} + 2 \cdot - 4 t^{2 + 4} - 5 t^{3} (7 t^{3}) - 5 t^{3} (- 4 t^{2})$

Step 2.1.5.3

Add $2$ and $4$ .

$14 t^{7} + 2 \cdot - 4 t^{6} - 5 t^{3} (7 t^{3}) - 5 t^{3} (- 4 t^{2})$

Step 2.1.6

Multiply $2$ by $- 4$ .

$14 t^{7} - 8 t^{6} - 5 t^{3} (7 t^{3}) - 5 t^{3} (- 4 t^{2})$

Step 2.1.7

Rewrite using the commutative property of multiplication.

$14 t^{7} - 8 t^{6} - 5 \cdot 7 t^{3} t^{3} - 5 t^{3} (- 4 t^{2})$

Step 2.1.8

Multiply $t^{3}$ by $t^{3}$ by adding the exponents.

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Step 2.1.8.1

Move $t^{3}$ .

$14 t^{7} - 8 t^{6} - 5 \cdot 7 (t^{3} t^{3}) - 5 t^{3} (- 4 t^{2})$

Step 2.1.8.2

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

$14 t^{7} - 8 t^{6} - 5 \cdot 7 t^{3 + 3} - 5 t^{3} (- 4 t^{2})$

Step 2.1.8.3

Add $3$ and $3$ .

$14 t^{7} - 8 t^{6} - 5 \cdot 7 t^{6} - 5 t^{3} (- 4 t^{2})$

Step 2.1.9

Multiply $- 5$ by $7$ .

$14 t^{7} - 8 t^{6} - 35 t^{6} - 5 t^{3} (- 4 t^{2})$

Step 2.1.10

Rewrite using the commutative property of multiplication.

$14 t^{7} - 8 t^{6} - 35 t^{6} - 5 \cdot - 4 t^{3} t^{2}$

Step 2.1.11

Multiply $t^{3}$ by $t^{2}$ by adding the exponents.

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Step 2.1.11.1

Move $t^{2}$ .

$14 t^{7} - 8 t^{6} - 35 t^{6} - 5 \cdot - 4 (t^{2} t^{3})$

Step 2.1.11.2

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

$14 t^{7} - 8 t^{6} - 35 t^{6} - 5 \cdot - 4 t^{2 + 3}$

Step 2.1.11.3

Add $2$ and $3$ .

$14 t^{7} - 8 t^{6} - 35 t^{6} - 5 \cdot - 4 t^{5}$

Step 2.1.12

Multiply $- 5$ by $- 4$ .

$14 t^{7} - 8 t^{6} - 35 t^{6} + 20 t^{5}$

Step 2.2

Subtract $35 t^{6}$ from $- 8 t^{6}$ .

$14 t^{7} - 43 t^{6} + 20 t^{5}$