Finite Math Examples

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

Step 1

Simplify and reorder the polynomial.

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Step 1.1

Expand $(x - 3 y) (4 x + 5 y)$ using the FOIL Method.

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Step 1.1.1

Apply the distributive property.

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

Step 1.1.2

Apply the distributive property.

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

Step 1.1.3

Apply the distributive property.

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

Step 1.2

Simplify and combine like terms.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Rewrite using the commutative property of multiplication.

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

Step 1.2.1.2

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

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Step 1.2.1.2.1

Move $x$ .

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

Step 1.2.1.2.2

Multiply $x$ by $x$ .

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

Step 1.2.1.3

Rewrite using the commutative property of multiplication.

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

Step 1.2.1.4

Rewrite using the commutative property of multiplication.

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

Step 1.2.1.5

Multiply $- 3$ by $4$ .

$4 x^{2} + 5 x y - 12 y x - 3 y (5 y)$

Step 1.2.1.6

Rewrite using the commutative property of multiplication.

$4 x^{2} + 5 x y - 12 y x - 3 \cdot 5 y \cdot y$

Step 1.2.1.7

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

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Step 1.2.1.7.1

Move $y$ .

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

Step 1.2.1.7.2

Multiply $y$ by $y$ .

$4 x^{2} + 5 x y - 12 y x - 3 \cdot 5 y^{2}$

Step 1.2.1.8

Multiply $- 3$ by $5$ .

$4 x^{2} + 5 x y - 12 y x - 15 y^{2}$

Step 1.2.2

Subtract $12 y x$ from $5 x y$ .

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Step 1.2.2.1

Move $y$ .

$4 x^{2} + 5 x y - 12 x y - 15 y^{2}$

Step 1.2.2.2

Subtract $12 x y$ from $5 x y$ .

$4 x^{2} - 7 x y - 15 y^{2}$

Step 2

The largest exponent is the degree of the polynomial.

$2$