%5E2.jpeg "(6m+2)^2")
Expanding (6m + 2)^2
In mathematics, expanding a squared expression like (6m + 2)^2 involves applying the distributive property (or the FOIL method) to multiply the expression by itself.
Understanding the Concept
The expression (6m + 2)^2 is equivalent to multiplying (6m + 2) by itself:
(6m + 2)^2 = (6m + 2) * (6m + 2)
Expanding the Expression
To expand the expression, we can use the FOIL method (First, Outer, Inner, Last):
- First: Multiply the first terms of each binomial: (6m * 6m) = 36m^2
- Outer: Multiply the outer terms of the binomials: (6m * 2) = 12m
- Inner: Multiply the inner terms of the binomials: (2 * 6m) = 12m
- Last: Multiply the last terms of each binomial: (2 * 2) = 4
Combining Like Terms
Now, we combine the like terms:
36m^2 + 12m + 12m + 4
This simplifies to:
36m^2 + 24m + 4
Therefore, the expanded form of (6m + 2)^2 is 36m^2 + 24m + 4.
Alternative Method
An alternative method is to use the square of a binomial formula:
(a + b)^2 = a^2 + 2ab + b^2
In this case, a = 6m and b = 2. Applying the formula:
(6m + 2)^2 = (6m)^2 + 2(6m)(2) + (2)^2
Simplifying:
(6m + 2)^2 = 36m^2 + 24m + 4
Conclusion
Both methods lead to the same expanded expression: 36m^2 + 24m + 4. Understanding these methods allows you to expand squared binomials effectively.