Video Transcript
Expand and simplify 𝑥 plus two
multiplied by 𝑥 plus two.
The expression we need to simplify
is the product of two binomials: 𝑥 plus two and 𝑥 plus two. To expand this product means we
need to multiply out the brackets. We can do this in a number of
different ways, such as using the vertical method or grid method. But the method we’re going to
demonstrate here is to take a systematic approach to ensuring we multiply each term
in the first binomial by each term in the second.
We begin by multiplying the first
term in each binomial together: 𝑥 multiplied by 𝑥, which is 𝑥 squared. Then, we multiply the first term in
the first binomial by the second term in the second. This is also known as multiplying
the terms on the outside of the product together. 𝑥 multiplied by two is two 𝑥. Next, we multiply the terms on the
inside of the product together: two multiplied by 𝑥, which is two 𝑥. And finally we multiply the last
term in each binomial together: two multiplied by two, which is four.
At this stage, we have four terms
in the expansion, as we should when multiplying the two terms of one binomial by the
two terms of another. We can then simplify this
expression by combining the like terms in the center. Two 𝑥 plus two 𝑥 is four 𝑥. We’ve therefore found that the
expanded and simplified form of 𝑥 plus two multiplied by 𝑥 plus two is 𝑥 squared
plus four 𝑥 plus four.
It’s worth pointing out that the
product we’ve simplified here is, in fact, a perfect square, as both factors are the
same. When we expand a perfect square of
the form 𝑥 plus 𝑎 squared, we obtain the simplified expression 𝑥 squared plus two
𝑎𝑥 plus 𝑎 squared. Here, the value of 𝑎 is two, and
we can confirm that the coefficient of 𝑥 is indeed equal to two times two. And the constant term, four, is
indeed equal to two squared.
