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(x+6)^2 Expand And Simplify

2 min read Jun 17, 2024
(x+6)^2 Expand And Simplify

Expanding and Simplifying (x + 6)^2

The expression (x + 6)^2 represents the square of the binomial (x + 6). To expand and simplify this expression, we can use the following methods:

1. Using the FOIL method:

  • First: Multiply the first terms of each binomial: x * x = x^2
  • Outer: Multiply the outer terms of the binomials: x * 6 = 6x
  • Inner: Multiply the inner terms of the binomials: 6 * x = 6x
  • Last: Multiply the last terms of each binomial: 6 * 6 = 36

Now, combine the terms: x^2 + 6x + 6x + 36

Finally, simplify by combining like terms: x^2 + 12x + 36

2. Using the square of a sum pattern:

This pattern states that (a + b)^2 = a^2 + 2ab + b^2.

Applying this to our problem: (x + 6)^2 = x^2 + 2(x)(6) + 6^2

Simplifying: x^2 + 12x + 36

Both methods lead to the same simplified expression: x^2 + 12x + 36.

Key points:

  • Expanding a squared binomial requires multiplying the binomial by itself.
  • Using the FOIL method or the square of a sum pattern provides a systematic way to expand and simplify the expression.
  • Combining like terms after expansion is crucial to obtain the simplified form.

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