Find each product. See Example 5. (4m + 2n)²

Verified step by step guidance

1. Recognize that the expression $(4m+2n{)}^2$ is a perfect square trinomial.
2. Recall the formula for squaring a binomial: $(a+b{)}^2=a^2+2ab+b^2$.
3. Identify $a=4m$ and $b=2n$ in the expression $(4m+2n{)}^2$.
4. Apply the formula: $(4m+2n{)}^2=(4m{)}^2+2(4m)(2n)+(2n{)}^2$.
5. Simplify each term: $(4m{)}^2=16m^2$, $2(4m)(2n)=16mn$, and $(2n{)}^2=4n^2$.

Key Concepts

Binomial Expansion

Binomial expansion refers to the process of expanding expressions that are raised to a power, particularly those in the form of (a + b)². The formula for this expansion is (a + b)² = a² + 2ab + b², which allows us to calculate the square of a binomial by squaring each term and adding twice the product of the two terms.

Algebraic Expressions

Algebraic expressions are mathematical phrases that can include numbers, variables, and operators. In the expression (4m + 2n)², '4m' and '2n' are terms that can be manipulated using algebraic rules. Understanding how to work with these expressions is crucial for performing operations like expansion and simplification.

Like Terms

Like terms are terms in an algebraic expression that have the same variable raised to the same power. When expanding expressions, it is important to identify and combine like terms to simplify the result. In the context of (4m + 2n)², after expansion, terms involving 'm' and 'n' will need to be grouped accordingly.