Expand the Expression: (2x+y)(x+3) Using Distribution Method

$(2x+y)(x+3)=$

To solve this problem, we'll apply the FOIL method for multiplying binomials:

• First: Multiply the first terms in each binomial: $(2x)(x) = 2x^2$.
• Outer: Multiply the outer terms in the product: $(2x)(3) = 6x$.
• Inner: Multiply the inner terms: $(y)(x) = xy$.
• Last: Multiply the last terms: $(y)(3) = 3y$.

Next, we combine these results to form the expanded expression:

$2x^2 + 6x + xy + 3y$.

Since terms $6x$ and $xy$ are not like terms, they cannot be combined, resulting in the final expression:

$2x^2 + xy + 6x + 3y$.

Upon reviewing the multiple-choice options, the correct answer is the expanded expression, choice 4: $2x^2 + xy + 6x + 3y$.