(5+6b^3)^2=

3 min read Jun 16, 2024

Expanding the Square of a Binomial: (5 + 6b^3)^2

This article will guide you through the process of expanding the expression (5 + 6b^3)^2.

Understanding the Concept

The expression (5 + 6b^3)^2 represents the square of a binomial. A binomial is an algebraic expression with two terms. To expand this, we can use the FOIL method or the square of a binomial formula.

Using the FOIL Method

The FOIL method stands for First, Outer, Inner, Last. It helps us multiply two binomials by systematically multiplying each term of the first binomial with each term of the second binomial.

Let's apply this to our problem:

First: Multiply the first terms of both binomials: 5 * 5 = 25
Outer: Multiply the outer terms: 5 * 6b^3 = 30b^3
Inner: Multiply the inner terms: 6b^3 * 5 = 30b^3
Last: Multiply the last terms: 6b^3 * 6b^3 = 36b^6

Now, combine all the terms: 25 + 30b^3 + 30b^3 + 36b^6

Finally, simplify the expression by combining like terms: 25 + 60b^3 + 36b^6

Using the Square of a Binomial Formula

The square of a binomial formula is: (a + b)^2 = a^2 + 2ab + b^2

Let's apply this to our problem:

a = 5
b = 6b^3

Now, substitute these values into the formula:

(5 + 6b^3)^2 = 5^2 + 2(5)(6b^3) + (6b^3)^2

Simplifying the expression:

(5 + 6b^3)^2 = 25 + 60b^3 + 36b^6

Conclusion

Therefore, the expanded form of (5 + 6b^3)^2 is 25 + 60b^3 + 36b^6. Both the FOIL method and the square of a binomial formula lead to the same answer. Choose the method that feels most comfortable and efficient for you.