%5E2-expand-and-simplify.jpeg "(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.