Expand using the Binomial Theorem (x-5)^2

${(x - 5)}^{2}$

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

$\sum_{k = 0}^{2} \frac{2!}{(2 - k)! k!} \cdot {(x)}^{2 - k} \cdot {(- 5)}^{k}$

Expand the summation.

$\frac{2!}{(2 - 0)! 0!} {(x)}^{2 - 0} \cdot {(- 5)}^{0} + \frac{2!}{(2 - 1)! 1!} {(x)}^{2 - 1} \cdot (- 5) + \frac{2!}{(2 - 2)! 2!} {(x)}^{2 - 2} \cdot {(- 5)}^{2}$

Simplify the exponents for each term of the expansion.

$1 \cdot {(x)}^{2} \cdot {(- 5)}^{0} + 2 \cdot (x) \cdot (- 5) + 1 \cdot {(x)}^{0} \cdot {(- 5)}^{2}$

Simplify each term.

Tap for more steps...

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

${(x)}^{2} \cdot {(- 5)}^{0} + 2 \cdot {(x)}^{1} \cdot {(- 5)}^{1} + 1 \cdot {(x)}^{0} \cdot {(- 5)}^{2}$

Anything raised to $0$ is $1$ .

$x^{2} \cdot 1 + 2 \cdot {(x)}^{1} \cdot {(- 5)}^{1} + 1 \cdot {(x)}^{0} \cdot {(- 5)}^{2}$

Multiply $x^{2}$ by $1$ .

$x^{2} + 2 \cdot {(x)}^{1} \cdot {(- 5)}^{1} + 1 \cdot {(x)}^{0} \cdot {(- 5)}^{2}$

Simplify.

$x^{2} + 2 \cdot x \cdot {(- 5)}^{1} + 1 \cdot {(x)}^{0} \cdot {(- 5)}^{2}$

Evaluate the exponent.

$x^{2} + 2 x \cdot - 5 + 1 \cdot {(x)}^{0} \cdot {(- 5)}^{2}$

Multiply $- 5$ by $2$ .

$x^{2} - 10 x + 1 \cdot {(x)}^{0} \cdot {(- 5)}^{2}$

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

$x^{2} - 10 x + {(x)}^{0} \cdot {(- 5)}^{2}$

Anything raised to $0$ is $1$ .

$x^{2} - 10 x + 1 \cdot {(- 5)}^{2}$

Multiply ${(- 5)}^{2}$ by $1$ .

$x^{2} - 10 x + {(- 5)}^{2}$

Raise $- 5$ to the power of $2$ .

$x^{2} - 10 x + 25$

Do you know how to Expand using the Binomial Theorem (x-5)^2? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

Calculate the Square Root square root of 13

Calculate the Square Root square root of 22

Evaluate 6/4

Graph y=(x+3)^2

Solve Using the Square Root Property -5x^2=11