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Example Question #1 : How To Multiply Polynomials
and
What is ?
so we multiply the two function to get the answer. We use
Example Question #1 : How To Multiply Polynomials
Find the product:
Find the product:
Step 1: Use the distributive property.
Step 2: Combine like terms.
Example Question #2 : How To Multiply Polynomials
represents a positive quantity; represents a negative quantity.
Evaluate
The correct answer is not among the other choices.
The first two binomials are the difference and the sum of the same two expressions, which, when multiplied, yield the difference of their squares:
Again, a sum is multiplied by a difference to yield a difference of squares, which by the Power of a Power Property, is equal to:
, so by the Power of a Power Property,
Also, , so we can now substitute accordingly:
Note that the signs of and are actually irrelevant to the problem.
Example Question #14 : Polynomials
represents a positive quantity; represents a negative quantity.
Evaluate .
can be recognized as the pattern conforming to that of the difference of two perfect cubes:
Additionally, by way of the Power of a Power Property,
, making a square root of , or 625; since is positive, so is , so
.
Similarly, is a square root of , or 64; since is negative, so is (as an odd power of a negative number is negative), so
.
Therefore, substituting:
.
Example Question #2 : How To Multiply Polynomials
and represent positive quantities.
Evaluate .
can be recognized as the pattern conforming to that of the difference of two perfect cubes:
Additionally,
and is positive, so
Using the product of radicals property, we see that
and
and is positive, so
,
and
Substituting for and , then collecting the like radicals,
.
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