Finite Math Examples

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

Step 1

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

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

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $2 x (2 x) + 2 x y + 2 x \cdot 3 + y (2 x) + y \cdot y + y \cdot 3 - 3 (2 x) - 3 y - 3 \cdot 3$ .

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Step 2.1.1

Reorder the factors in the terms $y \cdot 3$ and $- 3 y$ .

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

Step 2.1.2

Subtract $3 y$ from $3 y$ .

$2 x (2 x) + 2 x y + 2 x \cdot 3 + y (2 x) + y \cdot y - 3 (2 x) + 0 - 3 \cdot 3$

Step 2.1.3

Add $2 x (2 x) + 2 x y + 2 x \cdot 3 + y (2 x) + y \cdot y - 3 (2 x)$ and $0$ .

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

Step 2.2

Simplify each term.

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Step 2.2.1

Rewrite using the commutative property of multiplication.

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

Step 2.2.2

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

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Step 2.2.2.1

Move $x$ .

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

Step 2.2.2.2

Multiply $x$ by $x$ .

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

Step 2.2.3

Multiply $2$ by $2$ .

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

Step 2.2.4

Multiply $3$ by $2$ .

$4 x^{2} + 2 x y + 6 x + y (2 x) + y \cdot y - 3 (2 x) - 3 \cdot 3$

Step 2.2.5

Rewrite using the commutative property of multiplication.

$4 x^{2} + 2 x y + 6 x + 2 y x + y \cdot y - 3 (2 x) - 3 \cdot 3$

Step 2.2.6

Multiply $y$ by $y$ .

$4 x^{2} + 2 x y + 6 x + 2 y x + y^{2} - 3 (2 x) - 3 \cdot 3$

Step 2.2.7

Multiply $2$ by $- 3$ .

$4 x^{2} + 2 x y + 6 x + 2 y x + y^{2} - 6 x - 3 \cdot 3$

Step 2.2.8

Multiply $- 3$ by $3$ .

$4 x^{2} + 2 x y + 6 x + 2 y x + y^{2} - 6 x - 9$

Step 2.3

Combine the opposite terms in $4 x^{2} + 2 x y + 6 x + 2 y x + y^{2} - 6 x - 9$ .

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Step 2.3.1

Subtract $6 x$ from $6 x$ .

$4 x^{2} + 2 x y + 2 y x + y^{2} + 0 - 9$

Step 2.3.2

Add $4 x^{2} + 2 x y + 2 y x + y^{2}$ and $0$ .

$4 x^{2} + 2 x y + 2 y x + y^{2} - 9$

Step 3

Add $2 x y$ and $2 y x$ .

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Step 3.1

Move $y$ .

$4 x^{2} + 2 x y + 2 x y + y^{2} - 9$

Step 3.2

Add $2 x y$ and $2 x y$ .

$4 x^{2} + 4 x y + y^{2} - 9$