Algebra Examples

$y \leq {(x + 1)}^{3}$

Step 1

Simplify ${(x + 1)}^{3}$ .

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Step 1.1

Use the Binomial Theorem.

$y \leq x^{3} + 3 x^{2} \cdot 1 + 3 x \cdot 1^{2} + 1^{3}$

Step 1.2

Simplify each term.

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Step 1.2.1

Multiply $3$ by $1$ .

$y \leq x^{3} + 3 x^{2} + 3 x \cdot 1^{2} + 1^{3}$

Step 1.2.2

One to any power is one.

$y \leq x^{3} + 3 x^{2} + 3 x \cdot 1 + 1^{3}$

Step 1.2.3

Multiply $3$ by $1$ .

$y \leq x^{3} + 3 x^{2} + 3 x + 1^{3}$

Step 1.2.4

One to any power is one.

$y \leq x^{3} + 3 x^{2} + 3 x + 1$

Step 2

The equation is not linear, so a constant slope does not exist.

Not Linear

Step 3

Graph a solid line, then shade the area below the boundary line since $y$ is less than $x^{3} + 3 x^{2} + 3 x + 1$ .

$y \leq x^{3} + 3 x^{2} + 3 x + 1$

Step 4