Algebra Examples

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

Step 1

Simplify the polynomial, then reorder it left to right starting with the highest degree term.

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Step 1.1

Simplify each term.

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Step 1.1.1

Expand $(x - 2 y) (3 x + 5 y)$ using the FOIL Method.

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Step 1.1.1.1

Apply the distributive property.

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

Step 1.1.1.2

Apply the distributive property.

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

Step 1.1.1.3

Apply the distributive property.

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

Step 1.1.2

Simplify and combine like terms.

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Step 1.1.2.1

Simplify each term.

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Step 1.1.2.1.1

Rewrite using the commutative property of multiplication.

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

Step 1.1.2.1.2

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

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Step 1.1.2.1.2.1

Move $x$ .

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

Step 1.1.2.1.2.2

Multiply $x$ by $x$ .

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

Step 1.1.2.1.3

Rewrite using the commutative property of multiplication.

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

Step 1.1.2.1.4

Rewrite using the commutative property of multiplication.

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

Step 1.1.2.1.5

Multiply $- 2$ by $3$ .

$3 x^{2} + 5 x y - 6 y x - 2 y (5 y) + x y$

Step 1.1.2.1.6

Rewrite using the commutative property of multiplication.

$3 x^{2} + 5 x y - 6 y x - 2 \cdot 5 y \cdot y + x y$

Step 1.1.2.1.7

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

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Step 1.1.2.1.7.1

Move $y$ .

$3 x^{2} + 5 x y - 6 y x - 2 \cdot 5 (y \cdot y) + x y$

Step 1.1.2.1.7.2

Multiply $y$ by $y$ .

$3 x^{2} + 5 x y - 6 y x - 2 \cdot 5 y^{2} + x y$

Step 1.1.2.1.8

Multiply $- 2$ by $5$ .

$3 x^{2} + 5 x y - 6 y x - 10 y^{2} + x y$

Step 1.1.2.2

Subtract $6 y x$ from $5 x y$ .

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Step 1.1.2.2.1

Move $y$ .

$3 x^{2} + 5 x y - 6 x y - 10 y^{2} + x y$

Step 1.1.2.2.2

Subtract $6 x y$ from $5 x y$ .

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

Step 1.2

Combine the opposite terms in $3 x^{2} - x y - 10 y^{2} + x y$ .

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Step 1.2.1

Add $- x y$ and $x y$ .

$3 x^{2} - 10 y^{2} + 0$

Step 1.2.2

Add $3 x^{2} - 10 y^{2}$ and $0$ .

$3 x^{2} - 10 y^{2}$

Step 2

The degree of a polynomial is the highest degree of its terms.

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Step 2.1

Identify the exponents on the variables in each term, and add them together to find the degree of each term.

$3 x^{2} \to 2$

$- 10 y^{2} \to 2$

Step 2.2

The largest exponent is the degree of the polynomial.

$2$

Step 3

The leading term in a polynomial is the term with the highest degree.

$3 x^{2}$

Step 4

The leading coefficient of a polynomial is the coefficient of the leading term.

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Step 4.1

The leading term in a polynomial is the term with the highest degree.

$3 x^{2}$

Step 4.2

The leading coefficient in a polynomial is the coefficient of the leading term.

$3$

Step 5

List the results.

Polynomial Degree: $2$

Leading Term: $3 x^{2}$

Leading Coefficient: $3$