Gauthmath helps with your math. Welcome to Gauthmath. In this video, we're going to talk about the Snow Ball Effect on the Difference of Two Squares.
Before we jump to the snowball effect. Let's make sure that you are familiar with the difference of two squares.
A plus B times A minus B. Equals to A squared minus B squared.
Then, what's the Snowball Effect? Let's have a look at this expression.
We could get A squared minus B squared from these two factors.
The 3rd factor is A squared plus B squared. If we bring these down, we could get another difference of squares.
A to the fourth minus B to the fourth. Again, we bring the last factor down, we get another difference of squares. The result is A to the eighth minus B to the eighth.
Now, what if we put A to the eighth plus B to the eighth, right after A to the eighth minus B to the eighth.
Yes, you're right. We could get A to the sixteenth minus B to the sixteenth. Now that you could put even more factors to the expression, and find that this method always applies. Only the exponents of A and B, like a rolling snowball, become bigger and bigger.
This is the Snowball effect on the difference of two squares. We could use this method to work out problems like this. To find the product in this problem, we don't want to expand the parenthesis.
Instead, we find that it looks similar to the snowball example. Let's replace 1 with 1 squared. Here we replace 1 with 1 to the fourth. And then replace 1 with 1 to the eighth.
Now, number 9 is the A and number 1 is the B.
If we times the whole expression by 9 minus 1, it would be exactly the same as what we just worked out.
We already know that the previous result is A to the sixteenth minus B to the sixteenth. So the answer here should be 9 to the sixteenth minus 1 to the sixteenth. Which is 9 to the sixteenth minus 1, since 1 raised to any power equals 1.
Is this the final answer? Wowww, wait! Don't forget that you've multiplied the expression by 9 minus 1. To get rid of it, you'll have to divide it so that the left and right hand side could be equal.
And the final answer is 9 to the sixteenth minus 1 over 8. Ok, next time when you see a problem like this one, remember how we simplified it using the snowball effect