Question

Which among the following algebraic expressions cannot be further simplified?

• A. $3\times (a+b)+6ab+8a$
• B. $5x+4y+7\times (x+y)$
• C. $81p+49q+64r$
• D. $-1+3+5+6m$

Answer 1

The correct option is C $81p+49q+64r$

In option (a.), we have $3\times (a+b)+6ab+8a.$ on opening the bracket we get $3a+3b+6ab+8a.$ Now, we clearly see that $3a$ and $8a$ are like terms and hence, given expression can be simplified to $11a+3b+6ab.$

In option (b.), we have $5x+4y+7\times (x+y).$
on opening the bracket we get $5x+4y+7x+7y.$ Now, we clearly see that $5x$ and $7x;$ $4y$ and $7y$ are like terms and hence, given expression can be simplified to $12x+11y.$

In option (c.), we have $81p+49q+64r$. As all of the terms in this algebraic expression are unlike terms, it cannot be simplified any further.

In option (d.), we have $-1+3+5+6m$. This algebraic expression can be further simplified by adding the constant terms together. i.e. $-1+3+5+6m=6m+7$

Therefore, only the expression given in option(c.) cannot be further simplified.