Algebra Examples

${(x + 1)}^{3} \cdot {(x + 1)}^{4}$

Step 1

Multiply ${(x + 1)}^{3}$ by ${(x + 1)}^{4}$ by adding the exponents.

Tap for more steps...

Step 1.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(x + 1)}^{3 + 4}$

Step 1.2

Add $3$ and $4$ .

${(x + 1)}^{7}$

Step 2

Use the Binomial Theorem.

$x^{7} + 7 x^{6} \cdot 1 + 21 x^{5} \cdot 1^{2} + 35 x^{4} \cdot 1^{3} + 35 x^{3} \cdot 1^{4} + 21 x^{2} \cdot 1^{5} + 7 x \cdot 1^{6} + 1^{7}$

Step 3

Simplify each term.

Tap for more steps...

Step 3.1

Multiply $7$ by $1$ .

$x^{7} + 7 x^{6} + 21 x^{5} \cdot 1^{2} + 35 x^{4} \cdot 1^{3} + 35 x^{3} \cdot 1^{4} + 21 x^{2} \cdot 1^{5} + 7 x \cdot 1^{6} + 1^{7}$

Step 3.2

One to any power is one.

$x^{7} + 7 x^{6} + 21 x^{5} \cdot 1 + 35 x^{4} \cdot 1^{3} + 35 x^{3} \cdot 1^{4} + 21 x^{2} \cdot 1^{5} + 7 x \cdot 1^{6} + 1^{7}$

Step 3.3

Multiply $21$ by $1$ .

$x^{7} + 7 x^{6} + 21 x^{5} + 35 x^{4} \cdot 1^{3} + 35 x^{3} \cdot 1^{4} + 21 x^{2} \cdot 1^{5} + 7 x \cdot 1^{6} + 1^{7}$

Step 3.4

One to any power is one.

$x^{7} + 7 x^{6} + 21 x^{5} + 35 x^{4} \cdot 1 + 35 x^{3} \cdot 1^{4} + 21 x^{2} \cdot 1^{5} + 7 x \cdot 1^{6} + 1^{7}$

Step 3.5

Multiply $35$ by $1$ .

$x^{7} + 7 x^{6} + 21 x^{5} + 35 x^{4} + 35 x^{3} \cdot 1^{4} + 21 x^{2} \cdot 1^{5} + 7 x \cdot 1^{6} + 1^{7}$

Step 3.6

One to any power is one.

$x^{7} + 7 x^{6} + 21 x^{5} + 35 x^{4} + 35 x^{3} \cdot 1 + 21 x^{2} \cdot 1^{5} + 7 x \cdot 1^{6} + 1^{7}$

Step 3.7

Multiply $35$ by $1$ .

$x^{7} + 7 x^{6} + 21 x^{5} + 35 x^{4} + 35 x^{3} + 21 x^{2} \cdot 1^{5} + 7 x \cdot 1^{6} + 1^{7}$

Step 3.8

One to any power is one.

$x^{7} + 7 x^{6} + 21 x^{5} + 35 x^{4} + 35 x^{3} + 21 x^{2} \cdot 1 + 7 x \cdot 1^{6} + 1^{7}$

Step 3.9

Multiply $21$ by $1$ .

$x^{7} + 7 x^{6} + 21 x^{5} + 35 x^{4} + 35 x^{3} + 21 x^{2} + 7 x \cdot 1^{6} + 1^{7}$

Step 3.10

One to any power is one.

$x^{7} + 7 x^{6} + 21 x^{5} + 35 x^{4} + 35 x^{3} + 21 x^{2} + 7 x \cdot 1 + 1^{7}$

Step 3.11

Multiply $7$ by $1$ .

$x^{7} + 7 x^{6} + 21 x^{5} + 35 x^{4} + 35 x^{3} + 21 x^{2} + 7 x + 1^{7}$

Step 3.12

One to any power is one.

$x^{7} + 7 x^{6} + 21 x^{5} + 35 x^{4} + 35 x^{3} + 21 x^{2} + 7 x + 1$