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Video: Finding the Value of an Unknown by Factorizing the Difference of two Squares

Kathryn Kingham

If 𝑥² − 𝑎 = (𝑥 + 5)(𝑥 − 5), what is the value of 𝑎?

01:52

Video Transcript

If 𝑥 squared minus 𝑎 equals 𝑥 plus five times 𝑥 minus five, what is the value of 𝑎?

Here’s what we know. We know that 𝑥 squared minus 𝑎 is going to equal 𝑥 plus five times 𝑥 minus five. But to find out what the 𝑎 value is, we’ll need to multiply out 𝑥 plus five and 𝑥 minus five.

Starting with our first term, we’ll multiply 𝑥 times 𝑥 equals 𝑥 squared. 𝑥 times negative five equals negative five 𝑥. Five times 𝑥 equals five 𝑥. Five times negative five equals negative 25. We can bring down the first part of our problem: 𝑥 squared minus 𝑎.

I wanna us to look closely at these two middle terms. They say negative five 𝑥 or minus five 𝑥 plus five 𝑥. What is five 𝑥 minus five 𝑥? Negative five 𝑥 plus five 𝑥 equals zero. Those two middle terms drop out. They cancel each other out. 𝑥 squared minus 𝑎 equals 𝑥 squared plus zero minus 25. Or in completely simplified terms, 𝑥 squared minus 𝑎 equals 𝑥 squared minus 25. So we know for sure our 𝑎 value is 25.