Question

Which among the following expression on simplification gives a binomial?

• A. $4x+6y-3x+5y+7z$
• B. $5x(8z-9y)$
• C. $2x+3y-4x-3y$
• D. $7x(2a+3b+4c)$

Answer 1

The correct option is B $5x(8z-9y)$

In option (a.), we have $4x+6y-3x+5y+7z$
Combining the like terms:
$4x+6y-3x+5y+7z$
$=(4x-3x)+(6y+5y)+7z$
$=x+11y+7z$

$x+11y+7z$ cannot be simplified further as it contains all the unlike terms in it.
The simplified form of $4x+6y-3x+5y+7z$ is $x+11y+7z$, i.e. a trinomial.


In option (b.), we have $5x(8z-9y)$
Simplifying the product:
$5x(8z-9y)=(5x\times 8z)-(5x\times 9y)$
$=40xz-45xy$

$40xz-45xy$ cannot be simplified further as it contains all the unlike terms in it.
The simplified form of $5x(8z-9y)$ is $40xz-45xy$, i.e. a binomial.


In option (c.), we have $2x+3y-4x-3y$
Combining the like terms:
$2x+3y-4x-3y$
$=(2x-4x)+(3y-3y)$
$=-2x+0$
$=-2x$

The simplified form of $2x+3y-4x-3y$ is $-2x$, i.e. a monomial.


In option (d.), we have $7x(2a+3b+4c)$
Simplifying the product:
$7x(2a+3b+4c)$
$=(7x\times 2a)+(7x\times 3b)+(7x\times 4c)$
$=14ax+21bx+28cx$

$14ax+21bx+28cx$ cannot be simplified further as it contains all the unlike terms in it.
The simplified form of $7x(2a+3b+4c)$ is $14ax+21bx+28cx$, i.e. a trinomial.

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