Algebra Examples

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

Step 1

Apply the distributive property.

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

Step 2

Simplify.

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Step 2.1

Rewrite using the commutative property of multiplication.

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

Step 2.2

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

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Step 2.2.1

Move $t$ .

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

Step 2.2.2

Multiply $t$ by $t^{3}$ .

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Step 2.2.2.1

Raise $t$ to the power of $1$ .

$- 4 \cdot 3 t^{3} r - 4 (t^{1} t^{3}) (2 r) - 4 t^{3} (- 5 t^{2})$

Step 2.2.2.2

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

$- 4 \cdot 3 t^{3} r - 4 t^{1 + 3} (2 r) - 4 t^{3} (- 5 t^{2})$

Step 2.2.3

Add $1$ and $3$ .

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

Step 2.3

Rewrite using the commutative property of multiplication.

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

Step 3

Simplify each term.

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Step 3.1

Multiply $- 4$ by $3$ .

$- 12 t^{3} r - 4 t^{4} (2 r) - 4 \cdot - 5 t^{3} t^{2}$

Step 3.2

Rewrite using the commutative property of multiplication.

$- 12 t^{3} r - 4 \cdot 2 t^{4} r - 4 \cdot - 5 t^{3} t^{2}$

Step 3.3

Multiply $- 4$ by $2$ .

$- 12 t^{3} r - 8 t^{4} r - 4 \cdot - 5 t^{3} t^{2}$

Step 3.4

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

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Step 3.4.1

Move $t^{2}$ .

$- 12 t^{3} r - 8 t^{4} r - 4 \cdot - 5 (t^{2} t^{3})$

Step 3.4.2

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

$- 12 t^{3} r - 8 t^{4} r - 4 \cdot - 5 t^{2 + 3}$

Step 3.4.3

Add $2$ and $3$ .

$- 12 t^{3} r - 8 t^{4} r - 4 \cdot - 5 t^{5}$

Step 3.5

Multiply $- 4$ by $- 5$ .

$- 12 t^{3} r - 8 t^{4} r + 20 t^{5}$