Expand the Binomial Product: (2x+3y)(2z+12m) Step by Step

Question

(2x+3y)(2z+12m)= (2x+3y)(2z+12m)=

Video Solution

Step-by-Step Solution

Let's simplify the given expression, open the parentheses using the extended distribution law:

(a+b)(c+d)=ac+ad+bc+bd (\textcolor{red}{a}+\textcolor{blue}{b})(c+d)=\textcolor{red}{a}c+\textcolor{red}{a}d+\textcolor{blue}{b}c+\textcolor{blue}{b}d

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 laws of sign multiplication and thus we can present any expression in parentheses, which we 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:

(2x+3y)(2z+12m)2x2z+2x12m+3y2z+3y12m4xz+24xm+6yz+36ym (\textcolor{red}{2x}+\textcolor{blue}{3y})(2z+12m)\\ \textcolor{red}{2x}\cdot 2z+\textcolor{red}{2x}\cdot12m+\textcolor{blue}{3y}\cdot 2z+\textcolor{blue}{3y} \cdot12m\\ 4xz+24xm+6yz+36ym

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 z,m x and y, have identical exponents (in the absence of one of the variables from the expression, we'll consider its exponent as zero power, this is because any number raised to the power of zero equals 1),

Note that in the expression we got in the last step there are four different terms, this is because there isn't even one pair of terms where the (different) variables have the same exponent, therefore the expression we already got is the final and most simplified expression:
4xz+24xm+6yz+36ym \textcolor{purple}{ 4xz}\textcolor{green}{+24xm}\textcolor{black}{+6yz}\textcolor{orange}{+36ym }\\ 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 have therefore concluded that the correct answer is answer D.

Answer

4xz+24xm+6yz+36ym 4xz+24xm+6yz+36ym