Question

Solve the following:
Add \[ = 7xy + 5yz - 3zx,{\kern 1pt} {\kern 1pt} {\kern 1pt} 4yz + 9zx - 4y,{\kern 1pt} {\kern 1pt} - 3xz + {\kern 1pt} {\kern 1pt} {\kern 1pt} 5x - 2y\]

Answer 1

Hint: Watch out for the common terms from the given expressions and then use addition or subtraction accordingly to solve the given problem. Keep in mind about the alike terms and then perform the required operation.

Complete step-by-step solution:
We are given with the terms \[7xy + 5yz - 3zx,{\kern 1pt} {\kern 1pt} {\kern 1pt} 4yz + 9zx - 4y,{\kern 1pt} {\kern 1pt} - 3xz + {\kern 1pt} 5x - 2y\]and are asked to add the terms.
That is, \[7xy + 5yz - 3zx + 4yz + 9zx - 4y - 3xz + {\kern 1pt} {\kern 1pt} {\kern 1pt} 5x - 2y\]
Now let us take and write the common terms together (if any),
\[7xy + 5yz + 4yz - 3zx - 3xz + 9zx - 4y + {\kern 1pt} {\kern 1pt} {\kern 1pt} 5x - 2y\]
\[ = 7xy + 9yz + 3zx - 4y + {\kern 1pt} {\kern 1pt} {\kern 1pt} 5x - 2y\] \[(\because xz = zx)\]
Thus we obtain our final required solution for the given problem i.e. \[7xy + 9yz + 3zx - 4y + {\kern 1pt} {\kern 1pt} {\kern 1pt} 5x - 2y\]
Additional information: In Mathematics, we specifically have four primary operations: addition, subtraction, multiplication, and division. These can be finished on numbers and algebraic expressions. The addition and subtraction of algebraic expressions is almost similar to the addition and subtraction of numbers. However, in the case of algebraic expressions, we need to type and surround the like phrases and the no longer like terms collectively which makes it less complicated to simplify. To add two or greater monomials which are probably like terms, add the coefficients; hold the variables and exponents at the variables the same. To subtract or add more monomials that are like phrases, subtract the coefficients; maintain the variables and exponents at the variables and the identical.

Note: It is important that we treat the operations of addition, subtraction, multiplication and division as same as we treat the operations in numbers. It is also important that we know the commutativity of variables to perform the operations easily and in a faster way. This usage of operations lays the base of further mathematics and helps us solve other problems in mathematics.