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Kathryn Kingham

Factor the expression 𝑥² − 49.

Factor the expression 𝑥 squared minus 49.

Just take a look at these two values. We have 𝑥 squared and we have 49. Do you notice anything about these two numbers? 𝑥 squared is a square and 49 is a square. We can also notice that we’re subtracting a square from a square. We’re finding the difference of squares. And the formula for factoring the difference of squares looks like this; 𝑎 squared minus 𝑏 squared equals 𝑎 plus 𝑏 times 𝑎 minus 𝑏.

We can use that formula to help us factor 𝑥 squared minus 49. The square root of 𝑥 squared equals 𝑥. One of the factors will be an addition problem and the other factor will be a subtraction problem.

For our problem, 𝑏 squared equals 49. If I take the square root of 𝑏 squared and the square root of 49, I’ll find the value of 𝑏. Here, 𝑏 equals seven. To factor 𝑥 squared minus 49, we can break it into terms 𝑥 plus seven times 𝑥 minus seven. The first thing we did was recognize that we were taking the difference of two squares then we remembered the formula for factoring the difference of squares and used that formula to solve. Our final answer would be 𝑥 plus seven times 𝑥 minus seven.

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