Algebra Examples

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

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

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Step 1.1.1.1

Apply the distributive property.

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

Step 1.1.1.2

Apply the distributive property.

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

Step 1.1.1.3

Apply the distributive property.

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

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.

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

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 $x$ .

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

Step 1.1.2.1.2.2

Multiply $x$ by $x$ .

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

Step 1.1.2.1.3

Move $4$ to the left of $x$ .

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

Step 1.1.2.1.4

Multiply $5$ by $- 5$ .

$y = 5 x^{2} + 4 x - 25 x - 5 \cdot 4 - 5 x^{2}$

Step 1.1.2.1.5

Multiply $- 5$ by $4$ .

$y = 5 x^{2} + 4 x - 25 x - 20 - 5 x^{2}$

Step 1.1.2.2

Subtract $25 x$ from $4 x$ .

$y = 5 x^{2} - 21 x - 20 - 5 x^{2}$

Step 1.2

Combine the opposite terms in $5 x^{2} - 21 x - 20 - 5 x^{2}$ .

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Step 1.2.1

Subtract $5 x^{2}$ from $5 x^{2}$ .

$y = - 21 x - 20 + 0$

Step 1.2.2

Add $- 21 x - 20$ and $0$ .

$y = - 21 x - 20$

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.

$- 21 x \to 1$

$- 20 \to 0$

Step 2.2

The largest exponent is the degree of the polynomial.

$1$

Step 3

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

$- 21 x$

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.

$- 21 x$

Step 4.2

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

$- 21$

Step 5

List the results.

Polynomial Degree: $1$

Leading Term: $- 21 x$

Leading Coefficient: $- 21$