Question Video: Evaluating Algebraic Expressions Involving Algebraic Identities | Nagwa Question Video: Evaluating Algebraic Expressions Involving Algebraic Identities | Nagwa

# Question Video: Evaluating Algebraic Expressions Involving Algebraic Identities Mathematics • First Year of Preparatory School

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If (π₯ + π¦)Β² = 100 and π₯π¦ = 20, what is the value of π₯Β² + π¦Β²?

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### Video Transcript

If π₯ plus π¦ all squared is equal to 100 and π₯π¦ equals 20, what is the value of π₯ squared plus π¦ squared?

So, weβve been given two pieces of information about these numbers π₯ and π¦ and asked to use them to determine the value of π₯ squared plus π¦ squared. Now, your first thought may be that π₯ plus π¦ all squared is just equal to π₯ squared plus π¦ squared. In which case, the value weβre looking for is the value given in the question; itβs 100. But if this is the case, why have we also been given the value of π₯π¦?

In fact, if we were to answer the question this way, weβd have made one of the most common mistakes in mathematics because weβve incorrectly expanded the binomial. Remember that π₯ plus π¦ all squared means π₯ plus π¦ multiplied by π₯ plus π¦. So, we are, in fact, multiplying a binomial by itself, not just squaring each of the individual terms.

Letβs see what happens if we correctly expand π₯ plus π¦ all squared. Using the FOIL method which, remember, stands for firsts, outers, inners, lasts, this gives π₯ squared plus π₯π¦ plus π₯π¦ plus π¦ squared, which simplifies to π₯ squared plus two π₯π¦ plus π¦ squared. What we now have is an equation connecting π₯ plus π¦ all squared, whose value we know, π₯π¦, whose value we know, and π₯ squared plus π¦ squared, whose value we wish to calculate.

Substituting 100 for π₯ plus π¦ all squared and 20 for π₯π¦, we have 100 equals π₯ squared plus π¦ squared plus two multiplied by 20. That simplifies to 100 equals π₯ squared plus π¦ squared plus 40. And subtracting 40 from each side, we find that π₯ squared plus π¦ squared is equal to 60. So, weβve solved the problem. By correctly expanding the binomial π₯ plus π¦ all squared and then substituting the values given in the question, we found that π₯ squared plus π¦ squared is equal to 60.

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