Algebra Examples

$y = (x - 1) (4 x + 2) - 4 x^{2}$

Step 1

Simplify $(x - 1) (4 x + 2) - 4 x^{2}$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Expand $(x - 1) (4 x + 2)$ using the FOIL Method.

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Step 1.1.1.1

Apply the distributive property.

$y = x (4 x + 2) - 1 (4 x + 2) - 4 x^{2}$

Step 1.1.1.2

Apply the distributive property.

$y = x (4 x) + x \cdot 2 - 1 (4 x + 2) - 4 x^{2}$

Step 1.1.1.3

Apply the distributive property.

$y = x (4 x) + x \cdot 2 - 1 (4 x) - 1 \cdot 2 - 4 x^{2}$

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.

$y = 4 x \cdot x + x \cdot 2 - 1 (4 x) - 1 \cdot 2 - 4 x^{2}$

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 $x$ .

$y = 4 (x \cdot x) + x \cdot 2 - 1 (4 x) - 1 \cdot 2 - 4 x^{2}$

Step 1.1.2.1.2.2

Multiply $x$ by $x$ .

$y = 4 x^{2} + x \cdot 2 - 1 (4 x) - 1 \cdot 2 - 4 x^{2}$

Step 1.1.2.1.3

Move $2$ to the left of $x$ .

$y = 4 x^{2} + 2 \cdot x - 1 (4 x) - 1 \cdot 2 - 4 x^{2}$

Step 1.1.2.1.4

Multiply $4$ by $- 1$ .

$y = 4 x^{2} + 2 x - 4 x - 1 \cdot 2 - 4 x^{2}$

Step 1.1.2.1.5

Multiply $- 1$ by $2$ .

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

Step 1.1.2.2

Subtract $4 x$ from $2 x$ .

$y = 4 x^{2} - 2 x - 2 - 4 x^{2}$

Step 1.2

Combine the opposite terms in $4 x^{2} - 2 x - 2 - 4 x^{2}$ .

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Step 1.2.1

Subtract $4 x^{2}$ from $4 x^{2}$ .

$y = - 2 x - 2 + 0$

Step 1.2.2

Add $- 2 x - 2$ and $0$ .

$y = - 2 x - 2$

Step 2

A linear equation is an equation of a straight line, which means that the degree of a linear equation must be $0$ or $1$ for each of its variables. In this case, the degree of variable $y$ is $1$ and the degree of variable $x$ is $1$ .

Linear