Question

Which of the following is the simplified form of the algebraic expression $4x^3+\frac{x^3}{2}+x{y}^2+x^{2}y$

• A. $\frac{9x^3}{2}+x^2{y}^2$
• B. $\frac{9x^3}{2}+x{y}^2+x^{2}y$
• C. $\frac{9x^3}{2}+2x{y}^2$
• D. None of the above

Answer 1

The correct option is B $\frac{9x^3}{2}+x{y}^2+x^{2}y$

$4x^3$ & $\frac{x^3}{2}$ are like terms since both have the same unknown and equal corresponding exponents.
$\Rightarrow 4x^3+\frac{x^3}{2}=\frac{9x^3}{2}$

While $x{y}^2$ & $x^{2}y$ are unlike terms because both terms have the same unknowns but unequal corresponding exponents. We know that unlike terms can't be combined
$\therefore 4x^3+\frac{x^3}{2}+x{y}^2+x^{2}y=\frac{9x^3}{2}+x{y}^2+x^{2}y$