Question

Identify the term in the expression $x^3+4x^{2}y+7x{y}^2+y^3$ that contains $x^2,$ and write the coefficient of $x^2$ in that term.

• A. Term: $x^3$
  Coefficient: $x$
• B. Term: $4x^{2}y$
  Coefficient: $4y$
• C. Term: $4x^{2}y$
  Coefficient: $4x^{2}y$
• D. Term: $x^3$
  Coefficient: $x^3$

Answer 1

The correct option is B Term: $4x^{2}y$

Coefficient: $4y$
$\underset{–}{\text{Given}:}$
An expression: $x^3+4x^{2}y+7x{y}^2+y^3$

$\underset{–}{\text{Need to Find}:}$
The term containing $x^2,$ and the coefficient of $x^2$ in that term

We are given with an algebraic expression $x^3+4x^{2}y+7x{y}^2+y^3$.

The term containing $x^2$ in the given algebraic expression is $\underset{–}{4x^{2}y}$.

$4x^{2}y$ can be represented as:
$4x^{2}y=\left(4y\right)\times x^2=\left(4y\right)x^2$

$\therefore$ The coefficient of $x^2$ in $\left(4y\right)x^2$ is $\underset{–}{4y}.$

Hence, option (b.) is the correct answer.