Question

Which of the following polynomial is the result of given polynomial expression?

$a^3{b}^2(a^2-1)-a^{2}b(ab+a^{2}b+1)+a{b}^2(a^3-a^2+a)$

• A. $a^5{b}^2-3a^3{b}^4+a^2{b}^2+a^{2}b$
• B. $a^4{b}^2-3a^3{b}^2+a^2{b}^2-a{b}^{2}b$
• C. $a^5{b}^2-3a^3{b}^2+a^2{b}^2-a^{2}b$
• D. $a^4{b}^2-3a{b}^3{b}^2+a^2{b}^2-a^{2}b$

Answer 1

Answer: (C)

$a^5{b}^2-3a^3{b}^2+a^2{b}^2-a^{2}b$

$a^3{b}^2(a^2-1)-a^{2}b(ab+a^{2}b+1)+a{b}^2(a^3-a^2+a)$

$=a^5{b}^2-a^3{b}^2-a^3{b}^2-a^4{b}^2-a^{2}b+a^4{b}^2-a^3{b}^2+a^2{b}^2$

$=a^5{b}^2-3a^3{b}^2+a^2{b}^2-a^{2}b$

Hence option ${}^{\prime }{C}^{\prime }$ is the answer.

A polynomial is an expression consisting of variables and coefficient, that involves only the operations of addition, subtraction and multiplication, and non-negative integer exponents.
Therefore,
This is polynomial.