Category: Algebra
"Published in Newark, California, USA"
Write the product by inspection:
Solution:
Consider the given equation above
In order to get the product of two trinomials, we need to do the Distributive Property of Multiplication over Addition as follows
Another way in getting the product of two trinomials is by grouping of the terms into one group. Let's group the given equation and then get the product as follows
Since (4a - 2b) is consider as one term, then we can apply the product of two binomials for the above equation as follows
Expand and simplify the above equation, we have
The above answer is exactly the same by using the first method.
Category: Algebra
"Published in Suisun City, California, USA"
Write the product by inspection:
Solution:
Consider the given equation above
As you notice that the two binomials whose variables are exponents of a base which is 3. Let's treat them as whole variables in multiplying the terms. The above equation can be written as
Since the exponents of 3 are different, then we cannot combine those terms. Therefore, the final answer is
Category: Algebra
"Published in Suisun City, California, USA"
Remove the grouping symbols and simplify:
Solution:
Consider the given equation above
As you notice that the outer group is brace, then followed by bracket, and then parenthesis. Since the most inner group is parenthesis, then we have to remove the parenthesis first, then next is bracket, and the last is brace. Be careful when you are removing the group symbols especially with the coefficients and the signs as well. We can rewrite the above equation as follows
Therefore, the answer is
Category: Algebra
"Published in Suisun City, California, USA"
What polynomial should be multiplied by
to give
Solution:
The given problem above is about the division of a polynomial with another polynomial. We can rewrite the given problem above as follows
To perform the division, change the sign of the subtrahend and perform the addition in order to get the next term to be divided.
Therefore, the factor is
Category: Algebra
"Published in Suisun City, California, USA"
Multiply the following polynomials:
Solution:
Consider the given polynomial above
Combine similar terms of each grouped terms as follows
Apply the distributive property of multiplication over addition, we have
Therefore, the final answer is
Category: Algebra
"Published in Newark, California, USA"
Subtract the sum of the first two expressions from the sum of the remaining expressions:
Solution:
The first that we have to do is to group the subtrahend and minuend. The subtrahend is the sum of the first two polynomials while the minuend is the sum of the rest of the polynomials. Hence,
Change the sign of the subtrahend and perform the addition, we have
Therefore, the final answer is
Category: Algebra
"Published in Newark, California, USA"
Add the following polynomials:
Solution:
The first thing that we have to do is to group each term according to their variables. Like combines like. When you combine similar or like terms, please be very careful especially with the signs. Consider the given equation above
Since we will add all the given polynomials above, then we don't have to change the sign of each terms. Group the given polynomials according to their variables, we have
Therefore, the final answer is
