Chemistry Examples

$(8 x - 4 y + 2) (3 x + 2 y - 5)$

Step 1

Expand $(8 x - 4 y + 2) (3 x + 2 y - 5)$ by multiplying each term in the first expression by each term in the second expression.

$8 x (3 x) + 8 x (2 y) + 8 x \cdot - 5 - 4 y (3 x) - 4 y (2 y) - 4 y \cdot - 5 + 2 (3 x) + 2 (2 y) + 2 \cdot - 5$

Step 2

Simplify each term.

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Step 2.1

Rewrite using the commutative property of multiplication.

$8 \cdot 3 x \cdot x + 8 x (2 y) + 8 x \cdot - 5 - 4 y (3 x) - 4 y (2 y) - 4 y \cdot - 5 + 2 (3 x) + 2 (2 y) + 2 \cdot - 5$

Step 2.2

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

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Step 2.2.1

Move $x$ .

$8 \cdot 3 (x \cdot x) + 8 x (2 y) + 8 x \cdot - 5 - 4 y (3 x) - 4 y (2 y) - 4 y \cdot - 5 + 2 (3 x) + 2 (2 y) + 2 \cdot - 5$

Step 2.2.2

Multiply $x$ by $x$ .

$8 \cdot 3 x^{2} + 8 x (2 y) + 8 x \cdot - 5 - 4 y (3 x) - 4 y (2 y) - 4 y \cdot - 5 + 2 (3 x) + 2 (2 y) + 2 \cdot - 5$

Step 2.3

Multiply $8$ by $3$ .

$24 x^{2} + 8 x (2 y) + 8 x \cdot - 5 - 4 y (3 x) - 4 y (2 y) - 4 y \cdot - 5 + 2 (3 x) + 2 (2 y) + 2 \cdot - 5$

Step 2.4

Rewrite using the commutative property of multiplication.

$24 x^{2} + 8 \cdot 2 x y + 8 x \cdot - 5 - 4 y (3 x) - 4 y (2 y) - 4 y \cdot - 5 + 2 (3 x) + 2 (2 y) + 2 \cdot - 5$

Step 2.5

Multiply $8$ by $2$ .

$24 x^{2} + 16 x y + 8 x \cdot - 5 - 4 y (3 x) - 4 y (2 y) - 4 y \cdot - 5 + 2 (3 x) + 2 (2 y) + 2 \cdot - 5$

Step 2.6

Multiply $- 5$ by $8$ .

$24 x^{2} + 16 x y - 40 x - 4 y (3 x) - 4 y (2 y) - 4 y \cdot - 5 + 2 (3 x) + 2 (2 y) + 2 \cdot - 5$

Step 2.7

Rewrite using the commutative property of multiplication.

$24 x^{2} + 16 x y - 40 x - 4 \cdot 3 y x - 4 y (2 y) - 4 y \cdot - 5 + 2 (3 x) + 2 (2 y) + 2 \cdot - 5$

Step 2.8

Multiply $- 4$ by $3$ .

$24 x^{2} + 16 x y - 40 x - 12 y x - 4 y (2 y) - 4 y \cdot - 5 + 2 (3 x) + 2 (2 y) + 2 \cdot - 5$

Step 2.9

Rewrite using the commutative property of multiplication.

$24 x^{2} + 16 x y - 40 x - 12 y x - 4 \cdot 2 y \cdot y - 4 y \cdot - 5 + 2 (3 x) + 2 (2 y) + 2 \cdot - 5$

Step 2.10

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

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Step 2.10.1

Move $y$ .

$24 x^{2} + 16 x y - 40 x - 12 y x - 4 \cdot 2 (y \cdot y) - 4 y \cdot - 5 + 2 (3 x) + 2 (2 y) + 2 \cdot - 5$

Step 2.10.2

Multiply $y$ by $y$ .

$24 x^{2} + 16 x y - 40 x - 12 y x - 4 \cdot 2 y^{2} - 4 y \cdot - 5 + 2 (3 x) + 2 (2 y) + 2 \cdot - 5$

Step 2.11

Multiply $- 4$ by $2$ .

$24 x^{2} + 16 x y - 40 x - 12 y x - 8 y^{2} - 4 y \cdot - 5 + 2 (3 x) + 2 (2 y) + 2 \cdot - 5$

Step 2.12

Multiply $- 5$ by $- 4$ .

$24 x^{2} + 16 x y - 40 x - 12 y x - 8 y^{2} + 20 y + 2 (3 x) + 2 (2 y) + 2 \cdot - 5$

Step 2.13

Multiply $3$ by $2$ .

$24 x^{2} + 16 x y - 40 x - 12 y x - 8 y^{2} + 20 y + 6 x + 2 (2 y) + 2 \cdot - 5$

Step 2.14

Multiply $2$ by $2$ .

$24 x^{2} + 16 x y - 40 x - 12 y x - 8 y^{2} + 20 y + 6 x + 4 y + 2 \cdot - 5$

Step 2.15

Multiply $2$ by $- 5$ .

$24 x^{2} + 16 x y - 40 x - 12 y x - 8 y^{2} + 20 y + 6 x + 4 y - 10$

Step 3

Subtract $12 y x$ from $16 x y$ .

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Step 3.1

Move $y$ .

$24 x^{2} + 16 x y - 12 x y - 40 x - 8 y^{2} + 20 y + 6 x + 4 y - 10$

Step 3.2

Subtract $12 x y$ from $16 x y$ .

$24 x^{2} + 4 x y - 40 x - 8 y^{2} + 20 y + 6 x + 4 y - 10$

Step 4

Add $- 40 x$ and $6 x$ .

$24 x^{2} + 4 x y - 34 x - 8 y^{2} + 20 y + 4 y - 10$

Step 5

Add $20 y$ and $4 y$ .

$24 x^{2} + 4 x y - 34 x - 8 y^{2} + 24 y - 10$

Step 6

Move $- 34 x$ .

$24 x^{2} + 4 x y - 8 y^{2} - 34 x + 24 y - 10$