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The difference of squares pattern is:
To use this pattern on your expression, we need to be able to rewrite your expression (at least in our heads) as the sum of an "a" and a "b" times the difference of that "a" and "b". Once you realize that the "a" and "b" can be any Math expression, then you will become a more powerful user of patterns.
Here's how we can rewrite your expression:
Take a moment to see how this expression is equal to your original expression. Note how the minus in front of the parentheses in the second factor make the "-w" inside the parentheses equal to the "+w" in your original expression.
Once written this way, it is not hard to see that we have matched the difference of squares pattern (the left side) with the "a" being and the "b" being (v-w). So we can use the pattern to multiply, knowing that the answer will be difference of the squares of the "a" and the "b":
Squaring is simple. To square (v-w) we can use another pattern: :
Note the use of parentheses. That whole entire expression is . And if we were subtracting before then we need to subtract the whole expression when we replace .
One last simplification:
The alternative to using the pattern to multiply is to multiply the trinomials the "normal" way: Multiply each term of one polynomial by each term of the other and then add like terms,if any. This would mean 9 multiplications plus adding like terms. Using the patterns, once you learn how, makes this much easier.
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