Algebra Examples

${(x + 1)}^{4}$

Step 1

Use the Binomial Theorem.

$x^{4} + 4 x^{3} \cdot 1 + 6 x^{2} \cdot 1^{2} + 4 x \cdot 1^{3} + 1^{4}$

Step 2

Simplify each term.

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Multiply $4$ by $1$ .

$x^{4} + 4 x^{3} + 6 x^{2} \cdot 1^{2} + 4 x \cdot 1^{3} + 1^{4}$

One to any power is one.

$x^{4} + 4 x^{3} + 6 x^{2} \cdot 1 + 4 x \cdot 1^{3} + 1^{4}$

Multiply $6$ by $1$ .

$x^{4} + 4 x^{3} + 6 x^{2} + 4 x \cdot 1^{3} + 1^{4}$

One to any power is one.

$x^{4} + 4 x^{3} + 6 x^{2} + 4 x \cdot 1 + 1^{4}$

Multiply $4$ by $1$ .

$x^{4} + 4 x^{3} + 6 x^{2} + 4 x + 1^{4}$

One to any power is one.

$x^{4} + 4 x^{3} + 6 x^{2} + 4 x + 1$