Which of the following expressions is equivalent to $92 x^2+x-1+x y+\frac{2 x^3}{x}$?
A. $94 x^2+x+x y-1$
B. $92 x^2+3 x+x y-1$
C. $2 x^2+92 x+y-1$
D. $2 x^3+92 x^2+2 x+x y-1$
Answer (1)
Simplify the given expression by dividing 2 x 3 by x to get 2 x 2 . Combine like terms 92 x 2 and 2 x 2 to get 94 x 2 . The simplified expression is 94 x 2 + x + x y − 1 . The equivalent expression is 94 x 2 + x + x y − 1 .
Explanation
Understanding the Problem We are given the expression 92 x 2 + x − 1 + x y + x 2 x 3 and asked to find an equivalent expression from the given options.
Simplifying the Expression First, we simplify the term x 2 x 3 . Since x = 0 , we can divide 2 x 3 by x to get 2 x 2 . So the expression becomes 92 x 2 + x − 1 + x y + 2 x 2 .
Combining Like Terms Next, we combine like terms. We have 92 x 2 and 2 x 2 , which combine to give 94 x 2 . The expression now becomes 94 x 2 + x − 1 + x y .
Comparing with Options Rearranging the terms, we have 94 x 2 + x + x y − 1 . Now we compare this expression with the given options. Option A is 94 x 2 + x + x y − 1 , which matches our simplified expression.
Examples
Understanding how to simplify algebraic expressions is crucial in many fields, such as physics and engineering. For example, when calculating the trajectory of a projectile, you might start with a complex equation involving multiple terms. Simplifying this equation by combining like terms and reducing fractions can make the calculations much easier and more accurate. This skill is also essential in computer science for optimizing code and reducing computational complexity.
