%5E2-simplified.jpeg "(4x+5)^2 Simplified")
Simplifying (4x + 5)^2
The expression (4x + 5)^2 represents the square of the binomial (4x + 5). To simplify this, we can use the FOIL method or the square of a binomial pattern.
Using the FOIL Method
FOIL stands for First, Outer, Inner, Last. This method helps us multiply two binomials:
- First: Multiply the first terms of each binomial: (4x) * (4x) = 16x^2
- Outer: Multiply the outer terms of the binomials: (4x) * (5) = 20x
- Inner: Multiply the inner terms of the binomials: (5) * (4x) = 20x
- Last: Multiply the last terms of each binomial: (5) * (5) = 25
Now, combine the terms: 16x^2 + 20x + 20x + 25
Finally, simplify by combining like terms: 16x^2 + 40x + 25
Using the Square of a Binomial Pattern
The square of a binomial pattern states: (a + b)^2 = a^2 + 2ab + b^2
In our case, a = 4x and b = 5. Applying the pattern:
(4x + 5)^2 = (4x)^2 + 2(4x)(5) + (5)^2
Simplifying: 16x^2 + 40x + 25
Conclusion
Both methods lead to the same simplified expression: 16x^2 + 40x + 25. Remember, when dealing with squared binomials, using the appropriate pattern can save you time and effort.