Pre-Algebra Examples

$(5 x - y - z) (2 x + 3 y + 2 z)$

Step 1

Expand $(5 x - y - z) (2 x + 3 y + 2 z)$ by multiplying each term in the first expression by each term in the second expression.

$5 x (2 x) + 5 x (3 y) + 5 x (2 z) - y (2 x) - y (3 y) - y (2 z) - z (2 x) - z (3 y) - z (2 z)$

Step 2

Simplify each term.

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Step 2.1

Rewrite using the commutative property of multiplication.

$5 \cdot 2 x \cdot x + 5 x (3 y) + 5 x (2 z) - y (2 x) - y (3 y) - y (2 z) - z (2 x) - z (3 y) - z (2 z)$

Step 2.2

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

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Step 2.2.1

Move $x$ .

$5 \cdot 2 (x \cdot x) + 5 x (3 y) + 5 x (2 z) - y (2 x) - y (3 y) - y (2 z) - z (2 x) - z (3 y) - z (2 z)$

Step 2.2.2

Multiply $x$ by $x$ .

$5 \cdot 2 x^{2} + 5 x (3 y) + 5 x (2 z) - y (2 x) - y (3 y) - y (2 z) - z (2 x) - z (3 y) - z (2 z)$

Step 2.3

Multiply $5$ by $2$ .

$10 x^{2} + 5 x (3 y) + 5 x (2 z) - y (2 x) - y (3 y) - y (2 z) - z (2 x) - z (3 y) - z (2 z)$

Step 2.4

Rewrite using the commutative property of multiplication.

$10 x^{2} + 5 \cdot 3 x y + 5 x (2 z) - y (2 x) - y (3 y) - y (2 z) - z (2 x) - z (3 y) - z (2 z)$

Step 2.5

Multiply $5$ by $3$ .

$10 x^{2} + 15 x y + 5 x (2 z) - y (2 x) - y (3 y) - y (2 z) - z (2 x) - z (3 y) - z (2 z)$

Step 2.6

Rewrite using the commutative property of multiplication.

$10 x^{2} + 15 x y + 5 \cdot 2 x z - y (2 x) - y (3 y) - y (2 z) - z (2 x) - z (3 y) - z (2 z)$

Step 2.7

Multiply $5$ by $2$ .

$10 x^{2} + 15 x y + 10 x z - y (2 x) - y (3 y) - y (2 z) - z (2 x) - z (3 y) - z (2 z)$

Step 2.8

Rewrite using the commutative property of multiplication.

$10 x^{2} + 15 x y + 10 x z - 1 \cdot 2 y x - y (3 y) - y (2 z) - z (2 x) - z (3 y) - z (2 z)$

Step 2.9

Multiply $- 1$ by $2$ .

$10 x^{2} + 15 x y + 10 x z - 2 y x - y (3 y) - y (2 z) - z (2 x) - z (3 y) - z (2 z)$

Step 2.10

Rewrite using the commutative property of multiplication.

$10 x^{2} + 15 x y + 10 x z - 2 y x - 1 \cdot 3 y \cdot y - y (2 z) - z (2 x) - z (3 y) - z (2 z)$

Step 2.11

Multiply $y$ by $y$ by adding the exponents.

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Step 2.11.1

Move $y$ .

$10 x^{2} + 15 x y + 10 x z - 2 y x - 1 \cdot 3 (y \cdot y) - y (2 z) - z (2 x) - z (3 y) - z (2 z)$

Step 2.11.2

Multiply $y$ by $y$ .

$10 x^{2} + 15 x y + 10 x z - 2 y x - 1 \cdot 3 y^{2} - y (2 z) - z (2 x) - z (3 y) - z (2 z)$

Step 2.12

Multiply $- 1$ by $3$ .

$10 x^{2} + 15 x y + 10 x z - 2 y x - 3 y^{2} - y (2 z) - z (2 x) - z (3 y) - z (2 z)$

Step 2.13

Rewrite using the commutative property of multiplication.

$10 x^{2} + 15 x y + 10 x z - 2 y x - 3 y^{2} - 1 \cdot 2 y z - z (2 x) - z (3 y) - z (2 z)$

Step 2.14

Multiply $- 1$ by $2$ .

$10 x^{2} + 15 x y + 10 x z - 2 y x - 3 y^{2} - 2 y z - z (2 x) - z (3 y) - z (2 z)$

Step 2.15

Rewrite using the commutative property of multiplication.

$10 x^{2} + 15 x y + 10 x z - 2 y x - 3 y^{2} - 2 y z - 1 \cdot 2 z x - z (3 y) - z (2 z)$

Step 2.16

Multiply $- 1$ by $2$ .

$10 x^{2} + 15 x y + 10 x z - 2 y x - 3 y^{2} - 2 y z - 2 z x - z (3 y) - z (2 z)$

Step 2.17

Rewrite using the commutative property of multiplication.

$10 x^{2} + 15 x y + 10 x z - 2 y x - 3 y^{2} - 2 y z - 2 z x - 1 \cdot 3 z y - z (2 z)$

Step 2.18

Multiply $- 1$ by $3$ .

$10 x^{2} + 15 x y + 10 x z - 2 y x - 3 y^{2} - 2 y z - 2 z x - 3 z y - z (2 z)$

Step 2.19

Rewrite using the commutative property of multiplication.

$10 x^{2} + 15 x y + 10 x z - 2 y x - 3 y^{2} - 2 y z - 2 z x - 3 z y - 1 \cdot 2 z \cdot z$

Step 2.20

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

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Step 2.20.1

Move $z$ .

$10 x^{2} + 15 x y + 10 x z - 2 y x - 3 y^{2} - 2 y z - 2 z x - 3 z y - 1 \cdot 2 (z \cdot z)$

Step 2.20.2

Multiply $z$ by $z$ .

$10 x^{2} + 15 x y + 10 x z - 2 y x - 3 y^{2} - 2 y z - 2 z x - 3 z y - 1 \cdot 2 z^{2}$

Step 2.21

Multiply $- 1$ by $2$ .

$10 x^{2} + 15 x y + 10 x z - 2 y x - 3 y^{2} - 2 y z - 2 z x - 3 z y - 2 z^{2}$

Step 3

Subtract $2 y x$ from $15 x y$ .

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Step 3.1

Move $y$ .

$10 x^{2} + 15 x y - 2 x y + 10 x z - 3 y^{2} - 2 y z - 2 z x - 3 z y - 2 z^{2}$

Step 3.2

Subtract $2 x y$ from $15 x y$ .

$10 x^{2} + 13 x y + 10 x z - 3 y^{2} - 2 y z - 2 z x - 3 z y - 2 z^{2}$

Step 4

Subtract $2 z x$ from $10 x z$ .

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Step 4.1

Move $z$ .

$10 x^{2} + 13 x y - 3 y^{2} - 2 y z + 10 x z - 2 x z - 3 z y - 2 z^{2}$

Step 4.2

Subtract $2 x z$ from $10 x z$ .

$10 x^{2} + 13 x y - 3 y^{2} - 2 y z + 8 x z - 3 z y - 2 z^{2}$

Step 5

Subtract $3 z y$ from $- 2 y z$ .

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Step 5.1

Move $z$ .

$10 x^{2} + 13 x y - 3 y^{2} - 2 y z - 3 y z + 8 x z - 2 z^{2}$

Step 5.2

Subtract $3 y z$ from $- 2 y z$ .

$10 x^{2} + 13 x y - 3 y^{2} - 5 y z + 8 x z - 2 z^{2}$

Step 6

Move $- 5 y z$ .

$10 x^{2} + 13 x y - 3 y^{2} + 8 x z - 5 y z - 2 z^{2}$

Step 7

Move $- 3 y^{2}$ .

$10 x^{2} + 13 x y + 8 x z - 3 y^{2} - 5 y z - 2 z^{2}$