Question

There are 289x^2 students in a class out
of which 9y² students are late comers
on a particular day all the late comers of
the class were called by the Principal in
his office How many students left in
the class? factorise the expression hence
obtained.​

Answer 1

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Answer 2

Given:

No. of students in the class = $289x^{2}$

No. of latecomers = $9y^{2}$

To find:

No. of students left in the class when Principal called the latecomers to his office.

Solution:

Out of the $289x^{2}$ students in the class, $9y^{2}$ came late. These $9y^{2}$ students were called to the Principal's office. So, the remaining no. of students are $289x^{2} -9y^{2}$.

Here, $289x^{2}$ and $9y^{2}$ are perfect squares of $17x$ and $3y$. Also, this expression is of the form:

$a^{2}-b^{2}=(a-b)(a+b)$

where, $a^{2}$ and $b^{2}$ are  $289x^{2}$ and $9y^{2}$ respectively.

Hence,

$289x^{2} -9y^{2} =(17x-3y)(17x+3y)$

Hence, we obtained the factorised form of the expression.

The factorised form of the expression $289x^{2} -9y^{2}$ is $(17x-3y)(17x+3y)$.