Algebra Examples

$y = (x + 1) (6 x - 6) - 6 x^{2}$

Step 1

Simplify $(x + 1) (6 x - 6) - 6 x^{2}$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Expand $(x + 1) (6 x - 6)$ using the FOIL Method.

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Step 1.1.1.1

Apply the distributive property.

$y = x (6 x - 6) + 1 (6 x - 6) - 6 x^{2}$

Step 1.1.1.2

Apply the distributive property.

$y = x (6 x) + x \cdot - 6 + 1 (6 x - 6) - 6 x^{2}$

Step 1.1.1.3

Apply the distributive property.

$y = x (6 x) + x \cdot - 6 + 1 (6 x) + 1 \cdot - 6 - 6 x^{2}$

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.

$y = 6 x \cdot x + x \cdot - 6 + 1 (6 x) + 1 \cdot - 6 - 6 x^{2}$

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 $x$ .

$y = 6 (x \cdot x) + x \cdot - 6 + 1 (6 x) + 1 \cdot - 6 - 6 x^{2}$

Step 1.1.2.1.2.2

Multiply $x$ by $x$ .

$y = 6 x^{2} + x \cdot - 6 + 1 (6 x) + 1 \cdot - 6 - 6 x^{2}$

Step 1.1.2.1.3

Move $- 6$ to the left of $x$ .

$y = 6 x^{2} - 6 \cdot x + 1 (6 x) + 1 \cdot - 6 - 6 x^{2}$

Step 1.1.2.1.4

Multiply $6 x$ by $1$ .

$y = 6 x^{2} - 6 x + 6 x + 1 \cdot - 6 - 6 x^{2}$

Step 1.1.2.1.5

Multiply $- 6$ by $1$ .

$y = 6 x^{2} - 6 x + 6 x - 6 - 6 x^{2}$

Step 1.1.2.2

Add $- 6 x$ and $6 x$ .

$y = 6 x^{2} + 0 - 6 - 6 x^{2}$

Step 1.1.2.3

Add $6 x^{2}$ and $0$ .

$y = 6 x^{2} - 6 - 6 x^{2}$

Step 1.2

Combine the opposite terms in $6 x^{2} - 6 - 6 x^{2}$ .

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Step 1.2.1

Subtract $6 x^{2}$ from $6 x^{2}$ .

$y = 0 - 6$

Step 1.2.2

Subtract $6$ from $0$ .

$y = - 6$

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 $1$ .

Linear