Question

Solve:
$$xy - \left[ {yz - zx - yx - \left( {3y - xz} \right) - \left( {x - y - 2y} \right)} \right]$$

Answer 1

Hint: The given question has an algebraic expression. We need to solve it and bring it down to its simplest form. We observe that there are only negative signs present in the given problem and there are brackets. So, remove the brackets and start solving from inside. Then, we group the terms which are similar, simplify and get to the final answer. We need to remember the positive and negative sign rules.
$$ + \times + = + $$
$$ - \times - = + $$
$$ + \times - = - $$

Complete step-by-step answer:
Let us consider the given equation,
$$xy - \left[ {yz - zx - yx - \left( {3y - xz} \right) - \left( {x - y - 2y} \right)} \right]$$
Let us call the equation as A. That is,
$$A = xy - \left[ {yz - zx - yx - \left( {3y - xz} \right) - \left( {x - y - 2y} \right)} \right]$$
Now, let us start by opening the round brackets.
Using the above rule of signs, we get
$$ \Rightarrow A = xy - \left[ {yz - zx - yx - 3y + xz - x + y + 2y} \right]$$
Now, we have a lot of terms inside the square brackets. So, let us group them.
$$ \Rightarrow A = xy - \left[ {yz - yx - x - zx + xz - 3y + y + 2y} \right]$$
We can cancel out many terms from the above equation and simplify.
$$ \Rightarrow A = xy - \left[ {yz - yx - x - y + y} \right]$$
$$ \Rightarrow A = xy - \left[ {yz - yx - x} \right]$$
Now, we will remove the square brackets
$$ \Rightarrow A = xy - yz + yx + x$$
There are only two identical terms, so we add them
$$ \Rightarrow A = 2xy - yz + x$$
Therefore, the final answer for the given expression is $$2xy - yz + x$$

Note: The given expression contains simple terms. There is no multiplication sign, so they are all only one-degree polynomials. There are both round brackets and square brackets. So, first we need to simplify the terms inside the round brackets. If there is no simplification required, we can simplify it directly. Remember the rule for each sign. If there are similar terms, they get cancelled. For example, $$xy,yx$$ are the same term. Their places are interchanged. Since they have no positive or negative sign in between them, they give the same meaning.