Basic Math Examples

$(z + 2) (7 z^{3} - 4 z - z + 1)$

Step 1

Subtract $z$ from $- 4 z$ .

$(z + 2) (7 z^{3} - 5 z + 1)$

Step 2

Expand $(z + 2) (7 z^{3} - 5 z + 1)$ by multiplying each term in the first expression by each term in the second expression.

$z (7 z^{3}) + z (- 5 z) + z \cdot 1 + 2 (7 z^{3}) + 2 (- 5 z) + 2 \cdot 1$

Step 3

Simplify terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Rewrite using the commutative property of multiplication.

$7 z \cdot z^{3} + z (- 5 z) + z \cdot 1 + 2 (7 z^{3}) + 2 (- 5 z) + 2 \cdot 1$

Step 3.1.2

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

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Step 3.1.2.1

Move $z^{3}$ .

$7 (z^{3} z) + z (- 5 z) + z \cdot 1 + 2 (7 z^{3}) + 2 (- 5 z) + 2 \cdot 1$

Step 3.1.2.2

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

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Step 3.1.2.2.1

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

$7 (z^{3} z^{1}) + z (- 5 z) + z \cdot 1 + 2 (7 z^{3}) + 2 (- 5 z) + 2 \cdot 1$

Step 3.1.2.2.2

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

$7 z^{3 + 1} + z (- 5 z) + z \cdot 1 + 2 (7 z^{3}) + 2 (- 5 z) + 2 \cdot 1$

Step 3.1.2.3

Add $3$ and $1$ .

$7 z^{4} + z (- 5 z) + z \cdot 1 + 2 (7 z^{3}) + 2 (- 5 z) + 2 \cdot 1$

Step 3.1.3

Rewrite using the commutative property of multiplication.

$7 z^{4} - 5 z \cdot z + z \cdot 1 + 2 (7 z^{3}) + 2 (- 5 z) + 2 \cdot 1$

Step 3.1.4

Multiply $z$ by $z$ by adding the exponents.

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Step 3.1.4.1

Move $z$ .

$7 z^{4} - 5 (z \cdot z) + z \cdot 1 + 2 (7 z^{3}) + 2 (- 5 z) + 2 \cdot 1$

Step 3.1.4.2

Multiply $z$ by $z$ .

$7 z^{4} - 5 z^{2} + z \cdot 1 + 2 (7 z^{3}) + 2 (- 5 z) + 2 \cdot 1$

Step 3.1.5

Multiply $z$ by $1$ .

$7 z^{4} - 5 z^{2} + z + 2 (7 z^{3}) + 2 (- 5 z) + 2 \cdot 1$

Step 3.1.6

Multiply $7$ by $2$ .

$7 z^{4} - 5 z^{2} + z + 14 z^{3} + 2 (- 5 z) + 2 \cdot 1$

Step 3.1.7

Multiply $- 5$ by $2$ .

$7 z^{4} - 5 z^{2} + z + 14 z^{3} - 10 z + 2 \cdot 1$

Step 3.1.8

Multiply $2$ by $1$ .

$7 z^{4} - 5 z^{2} + z + 14 z^{3} - 10 z + 2$

Step 3.2

Simplify by adding terms.

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Step 3.2.1

Subtract $10 z$ from $z$ .

$7 z^{4} - 5 z^{2} + 14 z^{3} - 9 z + 2$

Step 3.2.2

Move $- 5 z^{2}$ .

$7 z^{4} + 14 z^{3} - 5 z^{2} - 9 z + 2$