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(k+5)^2

2 min read Jun 16, 2024
(k+5)^2

Understanding (k + 5)^2

(k + 5)^2 is a mathematical expression representing the square of the binomial (k + 5). This means multiplying the binomial by itself:

(k + 5)^2 = (k + 5)(k + 5)

To simplify this expression, we can use the FOIL method (First, Outer, Inner, Last). This method helps us multiply two binomials systematically.

Here's how it works:

  1. First: Multiply the first terms of each binomial: k * k = k^2
  2. Outer: Multiply the outer terms of the binomials: k * 5 = 5k
  3. Inner: Multiply the inner terms of the binomials: 5 * k = 5k
  4. Last: Multiply the last terms of each binomial: 5 * 5 = 25

Now, combine the results:

(k + 5)^2 = k^2 + 5k + 5k + 25

Finally, simplify by combining like terms:

(k + 5)^2 = k^2 + 10k + 25

Therefore, the expanded form of (k + 5)^2 is k^2 + 10k + 25.

Key Points:

  • The FOIL method is a useful tool for multiplying binomials.
  • Expanding a binomial square results in a trinomial (an expression with three terms).
  • The coefficient of the middle term (10k) is always twice the product of the terms in the original binomial (k and 5).
  • The constant term (25) is always the square of the second term in the original binomial (5).

Understanding how to expand expressions like (k + 5)^2 is essential in algebra and other areas of mathematics. It allows you to simplify expressions and solve equations more effectively.

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