(6m+2)^2

2 min read Jun 16, 2024
(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):

  1. First: Multiply the first terms of each binomial: (6m * 6m) = 36m^2
  2. Outer: Multiply the outer terms of the binomials: (6m * 2) = 12m
  3. Inner: Multiply the inner terms of the binomials: (2 * 6m) = 12m
  4. 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.

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