(x+y)(3x+2y)=
Let's simplify the given expression, open the parentheses using the extended distribution law:
Note that in the formula template for the above distribution law, we take by default that the operation between the terms inside the parentheses is addition, therefore we won't forget of course that the sign preceding the term is an inseparable part of it, we will also apply the rules of sign multiplication and thus we can present any expression in parentheses, which we'll open using the above formula, first as an expression where addition operation exists between all terms, in this expression as it's clear, all terms have a plus sign prefix, therefore we'll proceed directly to opening the parentheses,
Let's begin then with opening the parentheses:
In calculating the above multiplications, we used the multiplication table and the laws of exponents for multiplication between terms with identical bases:
In the next step we'll combine like terms, we'll define like terms as terms where the variable (or variables, each separately), in this case x and y, have identical exponents (in the absence of one of the variables from the expression, we'll treat its exponent as zero power, this is because raising any number to the zero power yields the result 1), we'll use the commutative law of addition, additionally we'll arrange the expression (if needed) from highest to lowest power from left to right (we'll treat the free number as zero power):
We highlighted the different terms using colors, and as emphasized before, we made sure that the sign preceding the term is an inseparable part of it,
We therefore concluded that the correct answer is answer A.