Video Transcript
Factorize fully 𝑥 squared minus
10𝑥𝑦 plus 25𝑦 squared.
In this question, we are given an
algebraic expression and asked to factor the expression fully. To do this, we can start by looking
at the expression we are asked to factor. We can see that the expression we
are given is a trinomial, since it is made up of three monomial terms. There are many ways to factor
trinomials. And they all start by checking to
see if the given trinomial matches any patterns that we already know how to
factor.
We could check for common factors
in the terms. However, we can note that this
trinomial is in the form of the perfect square of a binomial. In particular, consider the square
of 𝑥 minus 𝑘𝑦. We can expand and simplify to
obtain 𝑥 squared minus two 𝑘𝑥𝑦 plus 𝑘 squared 𝑦 squared. If we compare this to the
expression we are asked to factor, we can note that it is the same expression if we
set the value of 𝑘 equal to five. Therefore, we can substitute 𝑘
equals five into this formula to obtain that 𝑥 minus five 𝑦 all squared is equal
to 𝑥 squared minus 10𝑥𝑦 plus 25𝑦 squared.
We can verify that this is correct
by expanding the factored expression. If we do this, then we obtain the
expression confirming that this is the correct factorization. We can also note that we cannot
factor further since this is now the product of binomials, where the two terms share
no common factors. Hence, the answer is 𝑥 minus five
𝑦 all squared.
