Video Transcript
By factorizing or otherwise,
evaluate 10.1 squared minus 4.2 times 10.1 plus 2.1 squared.
In this question, we are asked to
evaluate an expression. We could evaluate this expression
by hand. However, it is easy to make a
mistake when multiplying decimal numbers. So, instead, let’s try to evaluate
this expression by first factoring the given expression.
We can start by noting that there
is no shared factors amongst the terms. Next, we can note that there are
three terms in the expression, and we can see that the first and last terms are
squares. Since the expression contains three
terms, we can compare the expression to trinomials that we know how to factor. Since the second term is negative,
we can compare the expression to the expansion of a perfect square of a
binomial. In particular, we recall that 𝑎
minus 𝑏 all squared is equal to 𝑎 squared minus two 𝑎𝑏 plus 𝑏 squared. We can then note that 4.2 is equal
to two times 2.1. We can then see that if we set 𝑎
equal to 10.1 and 𝑏 equal to 2.1, then the expression is exactly in the form of the
expansion of a perfect square of a binomial.
Therefore, we set 𝑎 equal to 10.1
and 𝑏 equal to 2.1 in the formula to factor the expression. We obtain 10.1 minus 2.1 all
squared. Finally, we have that 10.1 minus
2.1 is eight. So the expression simplifies to
give eight squared, which we can calculate is equal to 64.
