Question Video: Factorizing Perfect Square Trinomials | Nagwa Question Video: Factorizing Perfect Square Trinomials | Nagwa

Question Video: Factorizing Perfect Square Trinomials Mathematics • Second Year of Preparatory School

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Factorise fully 𝑥² − 10𝑥𝑦 + 25𝑦².

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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.

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