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

If π‘₯Β² βˆ’ π‘Ž = (π‘₯ + 5)(π‘₯ βˆ’ 5), what is the value of π‘Ž?

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Video Transcript

If π‘₯ squared minus π‘Ž equals π‘₯ plus five times π‘₯ minus five, what is the value of π‘Ž?

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

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

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

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