Algebra Examples

$(7.8 x - 3.4 y + z) (- 9.2 x + 4.8 y - 2.1 z)$

Step 1

Expand $(7.8 x - 3.4 y + z) (- 9.2 x + 4.8 y - 2.1 z)$ by multiplying each term in the first expression by each term in the second expression.

$7.8 x (- 9.2 x) + 7.8 x (4.8 y) + 7.8 x (- 2.1 z) - 3.4 y (- 9.2 x) - 3.4 y (4.8 y) - 3.4 y (- 2.1 z) + z (- 9.2 x) + z (4.8 y) + z (- 2.1 z)$

Step 2

Simplify each term.

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Step 2.1

Rewrite using the commutative property of multiplication.

$7.8 \cdot - 9.2 x \cdot x + 7.8 x (4.8 y) + 7.8 x (- 2.1 z) - 3.4 y (- 9.2 x) - 3.4 y (4.8 y) - 3.4 y (- 2.1 z) + z (- 9.2 x) + z (4.8 y) + z (- 2.1 z)$

Step 2.2

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

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Step 2.2.1

Move $x$ .

$7.8 \cdot - 9.2 (x \cdot x) + 7.8 x (4.8 y) + 7.8 x (- 2.1 z) - 3.4 y (- 9.2 x) - 3.4 y (4.8 y) - 3.4 y (- 2.1 z) + z (- 9.2 x) + z (4.8 y) + z (- 2.1 z)$

Step 2.2.2

Multiply $x$ by $x$ .

$7.8 \cdot - 9.2 x^{2} + 7.8 x (4.8 y) + 7.8 x (- 2.1 z) - 3.4 y (- 9.2 x) - 3.4 y (4.8 y) - 3.4 y (- 2.1 z) + z (- 9.2 x) + z (4.8 y) + z (- 2.1 z)$

Step 2.3

Multiply $7.8$ by $- 9.2$ .

$- 71.76 x^{2} + 7.8 x (4.8 y) + 7.8 x (- 2.1 z) - 3.4 y (- 9.2 x) - 3.4 y (4.8 y) - 3.4 y (- 2.1 z) + z (- 9.2 x) + z (4.8 y) + z (- 2.1 z)$

Step 2.4

Rewrite using the commutative property of multiplication.

$- 71.76 x^{2} + 7.8 \cdot 4.8 x y + 7.8 x (- 2.1 z) - 3.4 y (- 9.2 x) - 3.4 y (4.8 y) - 3.4 y (- 2.1 z) + z (- 9.2 x) + z (4.8 y) + z (- 2.1 z)$

Step 2.5

Multiply $7.8$ by $4.8$ .

$- 71.76 x^{2} + 37.44 x y + 7.8 x (- 2.1 z) - 3.4 y (- 9.2 x) - 3.4 y (4.8 y) - 3.4 y (- 2.1 z) + z (- 9.2 x) + z (4.8 y) + z (- 2.1 z)$

Step 2.6

Rewrite using the commutative property of multiplication.

$- 71.76 x^{2} + 37.44 x y + 7.8 \cdot - 2.1 x z - 3.4 y (- 9.2 x) - 3.4 y (4.8 y) - 3.4 y (- 2.1 z) + z (- 9.2 x) + z (4.8 y) + z (- 2.1 z)$

Step 2.7

Multiply $7.8$ by $- 2.1$ .

$- 71.76 x^{2} + 37.44 x y - 16.38 x z - 3.4 y (- 9.2 x) - 3.4 y (4.8 y) - 3.4 y (- 2.1 z) + z (- 9.2 x) + z (4.8 y) + z (- 2.1 z)$

Step 2.8

Rewrite using the commutative property of multiplication.

$- 71.76 x^{2} + 37.44 x y - 16.38 x z - 3.4 \cdot - 9.2 y x - 3.4 y (4.8 y) - 3.4 y (- 2.1 z) + z (- 9.2 x) + z (4.8 y) + z (- 2.1 z)$

Step 2.9

Multiply $- 3.4$ by $- 9.2$ .

$- 71.76 x^{2} + 37.44 x y - 16.38 x z + 31.28 y x - 3.4 y (4.8 y) - 3.4 y (- 2.1 z) + z (- 9.2 x) + z (4.8 y) + z (- 2.1 z)$

Step 2.10

Rewrite using the commutative property of multiplication.

$- 71.76 x^{2} + 37.44 x y - 16.38 x z + 31.28 y x - 3.4 \cdot 4.8 y \cdot y - 3.4 y (- 2.1 z) + z (- 9.2 x) + z (4.8 y) + z (- 2.1 z)$

Step 2.11

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

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Step 2.11.1

Move $y$ .

$- 71.76 x^{2} + 37.44 x y - 16.38 x z + 31.28 y x - 3.4 \cdot 4.8 (y \cdot y) - 3.4 y (- 2.1 z) + z (- 9.2 x) + z (4.8 y) + z (- 2.1 z)$

Step 2.11.2

Multiply $y$ by $y$ .

$- 71.76 x^{2} + 37.44 x y - 16.38 x z + 31.28 y x - 3.4 \cdot 4.8 y^{2} - 3.4 y (- 2.1 z) + z (- 9.2 x) + z (4.8 y) + z (- 2.1 z)$

Step 2.12

Multiply $- 3.4$ by $4.8$ .

$- 71.76 x^{2} + 37.44 x y - 16.38 x z + 31.28 y x - 16.32 y^{2} - 3.4 y (- 2.1 z) + z (- 9.2 x) + z (4.8 y) + z (- 2.1 z)$

Step 2.13

Rewrite using the commutative property of multiplication.

$- 71.76 x^{2} + 37.44 x y - 16.38 x z + 31.28 y x - 16.32 y^{2} - 3.4 \cdot - 2.1 y z + z (- 9.2 x) + z (4.8 y) + z (- 2.1 z)$

Step 2.14

Multiply $- 3.4$ by $- 2.1$ .

$- 71.76 x^{2} + 37.44 x y - 16.38 x z + 31.28 y x - 16.32 y^{2} + 7.14 y z + z (- 9.2 x) + z (4.8 y) + z (- 2.1 z)$

Step 2.15

Rewrite using the commutative property of multiplication.

$- 71.76 x^{2} + 37.44 x y - 16.38 x z + 31.28 y x - 16.32 y^{2} + 7.14 y z - 9.2 z x + z (4.8 y) + z (- 2.1 z)$

Step 2.16

Rewrite using the commutative property of multiplication.

$- 71.76 x^{2} + 37.44 x y - 16.38 x z + 31.28 y x - 16.32 y^{2} + 7.14 y z - 9.2 z x + 4.8 z y + z (- 2.1 z)$

Step 2.17

Rewrite using the commutative property of multiplication.

$- 71.76 x^{2} + 37.44 x y - 16.38 x z + 31.28 y x - 16.32 y^{2} + 7.14 y z - 9.2 z x + 4.8 z y - 2.1 z \cdot z$

Step 2.18

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

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Step 2.18.1

Move $z$ .

$- 71.76 x^{2} + 37.44 x y - 16.38 x z + 31.28 y x - 16.32 y^{2} + 7.14 y z - 9.2 z x + 4.8 z y - 2.1 (z \cdot z)$

Step 2.18.2

Multiply $z$ by $z$ .

$- 71.76 x^{2} + 37.44 x y - 16.38 x z + 31.28 y x - 16.32 y^{2} + 7.14 y z - 9.2 z x + 4.8 z y - 2.1 z^{2}$

Step 3

Add $37.44 x y$ and $31.28 y x$ .

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Step 3.1

Move $y$ .

$- 71.76 x^{2} + 37.44 x y + 31.28 x y - 16.38 x z - 16.32 y^{2} + 7.14 y z - 9.2 z x + 4.8 z y - 2.1 z^{2}$

Step 3.2

Add $37.44 x y$ and $31.28 x y$ .

$- 71.76 x^{2} + 68.72 x y - 16.38 x z - 16.32 y^{2} + 7.14 y z - 9.2 z x + 4.8 z y - 2.1 z^{2}$

Step 4

Subtract $9.2 z x$ from $- 16.38 x z$ .

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Step 4.1

Move $z$ .

$- 71.76 x^{2} + 68.72 x y - 16.32 y^{2} + 7.14 y z - 16.38 x z - 9.2 x z + 4.8 z y - 2.1 z^{2}$

Step 4.2

Subtract $9.2 x z$ from $- 16.38 x z$ .

$- 71.76 x^{2} + 68.72 x y - 16.32 y^{2} + 7.14 y z - 25.58 x z + 4.8 z y - 2.1 z^{2}$

Step 5

Add $7.14 y z$ and $4.8 z y$ .

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Step 5.1

Move $z$ .

$- 71.76 x^{2} + 68.72 x y - 16.32 y^{2} + 7.14 y z + 4.8 y z - 25.58 x z - 2.1 z^{2}$

Step 5.2

Add $7.14 y z$ and $4.8 y z$ .

$- 71.76 x^{2} + 68.72 x y - 16.32 y^{2} + 11.94 y z - 25.58 x z - 2.1 z^{2}$