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

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

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

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

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

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

Question