%5E2.jpeg "(x+12)^2")
Expanding (x + 12)^2
The expression (x + 12)^2 represents the square of the binomial (x + 12). To expand this expression, we can use the FOIL method or the square of a binomial formula.
Using the FOIL Method
FOIL stands for First, Outer, Inner, Last, and it's a way to multiply two binomials.
- First: Multiply the first terms of each binomial: x * x = x^2
- Outer: Multiply the outer terms of the binomials: x * 12 = 12x
- Inner: Multiply the inner terms of the binomials: 12 * x = 12x
- Last: Multiply the last terms of each binomial: 12 * 12 = 144
Now, combine the terms: x^2 + 12x + 12x + 144
Simplify by combining the like terms: x^2 + 24x + 144
Using the Square of a Binomial Formula
The square of a binomial formula states: (a + b)^2 = a^2 + 2ab + b^2
In this case, a = x and b = 12.
Applying the formula: (x + 12)^2 = x^2 + 2(x)(12) + 12^2
Simplifying: x^2 + 24x + 144
Conclusion
Both methods lead to the same expanded form of (x + 12)^2, which is x^2 + 24x + 144. You can choose whichever method you find easier to apply. Understanding these methods will be helpful for expanding other binomial expressions and solving various algebraic problems.