Expand Using the Binomial Theorem (13-2x)^2

${(13 - 2 x)}^{2}$

Step 1

Use the binomial expansion theorem to find each term. The binomial theorem states ${(a + b)}^{n} = \sum_{k = 0}^{n} n C k \cdot (a^{n - k} b^{k})$ .

$\sum_{k = 0}^{2} \frac{2!}{(2 - k)! k!} \cdot {(13)}^{2 - k} \cdot {(- 2 x)}^{k}$

Step 2

Expand the summation.

$\frac{2!}{(2 - 0)! 0!} \cdot {(13)}^{2 - 0} \cdot {(- 2 x)}^{0} + \frac{2!}{(2 - 1)! 1!} \cdot {(13)}^{2 - 1} \cdot {(- 2 x)}^{1} + \frac{2!}{(2 - 2)! 2!} \cdot {(13)}^{2 - 2} \cdot {(- 2 x)}^{2}$

Step 3

Simplify the exponents for each term of the expansion.

$1 \cdot {(13)}^{2} \cdot {(- 2 x)}^{0} + 2 \cdot {(13)}^{1} \cdot {(- 2 x)}^{1} + 1 \cdot {(13)}^{0} \cdot {(- 2 x)}^{2}$

Step 4

Simplify each term.

Multiply ${(13)}^{2}$ by $1$ .

${(13)}^{2} \cdot {(- 2 x)}^{0} + 2 \cdot {(13)}^{1} \cdot {(- 2 x)}^{1} + 1 \cdot {(13)}^{0} \cdot {(- 2 x)}^{2}$

Raise $13$ to the power of $2$ .

$169 \cdot {(- 2 x)}^{0} + 2 \cdot {(13)}^{1} \cdot {(- 2 x)}^{1} + 1 \cdot {(13)}^{0} \cdot {(- 2 x)}^{2}$

Apply the product rule to $- 2 x$ .

$169 \cdot ({(- 2)}^{0} x^{0}) + 2 \cdot {(13)}^{1} \cdot {(- 2 x)}^{1} + 1 \cdot {(13)}^{0} \cdot {(- 2 x)}^{2}$

Anything raised to $0$ is $1$ .

$169 \cdot (1 x^{0}) + 2 \cdot {(13)}^{1} \cdot {(- 2 x)}^{1} + 1 \cdot {(13)}^{0} \cdot {(- 2 x)}^{2}$

Multiply $x^{0}$ by $1$ .

$169 \cdot x^{0} + 2 \cdot {(13)}^{1} \cdot {(- 2 x)}^{1} + 1 \cdot {(13)}^{0} \cdot {(- 2 x)}^{2}$

Anything raised to $0$ is $1$ .

$169 \cdot 1 + 2 \cdot {(13)}^{1} \cdot {(- 2 x)}^{1} + 1 \cdot {(13)}^{0} \cdot {(- 2 x)}^{2}$

Multiply $169$ by $1$ .

$169 + 2 \cdot {(13)}^{1} \cdot {(- 2 x)}^{1} + 1 \cdot {(13)}^{0} \cdot {(- 2 x)}^{2}$

Evaluate the exponent.

$169 + 2 \cdot 13 \cdot {(- 2 x)}^{1} + 1 \cdot {(13)}^{0} \cdot {(- 2 x)}^{2}$

Multiply $2$ by $13$ .

$169 + 26 \cdot {(- 2 x)}^{1} + 1 \cdot {(13)}^{0} \cdot {(- 2 x)}^{2}$

Simplify.

$169 + 26 \cdot (- 2 x) + 1 \cdot {(13)}^{0} \cdot {(- 2 x)}^{2}$

Multiply $- 2$ by $26$ .

$169 - 52 x + 1 \cdot {(13)}^{0} \cdot {(- 2 x)}^{2}$

Multiply ${(13)}^{0}$ by $1$ .

$169 - 52 x + {(13)}^{0} \cdot {(- 2 x)}^{2}$

Anything raised to $0$ is $1$ .

$169 - 52 x + 1 \cdot {(- 2 x)}^{2}$

Multiply ${(- 2 x)}^{2}$ by $1$ .

$169 - 52 x + {(- 2 x)}^{2}$

Apply the product rule to $- 2 x$ .

$169 - 52 x + {(- 2)}^{2} x^{2}$

Raise $- 2$ to the power of $2$ .

$169 - 52 x + 4 x^{2}$

Expand Using the Binomial Theorem (13-2x)^2

Related Questions

Support LCMGCF.com by disabling your adblocker.