Video Transcript
Expand the product two π plus π
multiplied by two π minus π.
The expression weβve been asked to
expand is the product of two binomials: two π plus π and two π minus π. To expand this product means we
need to multiply out the brackets, also known as distributing the parentheses. When we do so, we need to ensure we
multiply each term in the first binomial by each term in the second. We can do this in a number of
different ways. But the method weβll demonstrate
here is called the vertical method. This is similar to the column
method for multiplying integers.
We begin by writing one factor
below the other and then find the product of each pair of terms. We start by multiplying each term
in the binomial two π plus π by negative π. Two π multiplied by negative π is
negative two ππ, and π multiplied by negative π is negative π squared. Next, we multiply each term in the
binomial two π plus π by the other term in the second binomial, two π. Two π multiplied by two π is four
π squared, and π multiplied by two π is two ππ.
We now add these four terms
together. Note that negative two ππ plus
two ππ is zero. So these terms cancel, and the sum
is four π squared minus π squared. Therefore, weβve found that the
expanded form of the product of two π plus π and two π minus π is four π
squared minus π squared.
Itβs worth noting that this
expression can also be written as two π all squared minus π squared. This is known as a difference of
two squares. This question illustrates the
general result that the product of π₯ plus π¦ and π₯ minus π¦ is always equal to π₯
squared minus π¦ squared.