Question

Add $5{x^2} - 7x + 3, - 8{x^2} + 2x - 5{\text{ and 7}}{{\text{x}}^2} - x - 2$.
$\left( a \right){\text{ }}4{x^2} - 7x + 3$
$\left( b \right){\text{ }}4{x^2} - 6x - 4$
$\left( c \right){\text{ }}4{x^2} - 7x - 4$
$\left( d \right){\text{ }}4{x^2} - 6x - 3$

Answer 1

Hint:
For solving this type of question we just need to first arrange the like terms together and then we have to move the like terms together and afterward add or deduct their coefficients. And in this, we can easily solve the problem.

Complete step by step solution:
To improve a mathematical expression that comprises both like and not at all like terms, we have to move the like terms together and afterward add or take away their coefficients. Here we will take the terms in braces so that we don’t get confused while expanding and rearranging the like terms together.
So according to the question we have the terms which are$5{x^2} - 7x + 3, - 8{x^2} + 2x - 5{\text{ and 7}}{{\text{x}}^2} - x - 2$. And we have to add these terms.
Therefore first of all we will rearrange the terms with like terms together and add those terms as we have to add.
\[ \Rightarrow \left( {5{x^2} - 7x + 3} \right){\text{ + }}\left( { - 8{x^2} + 2x - 5} \right) + \left( {{\text{7}}{{\text{x}}^2} - x - 2} \right)\]
Now on rearranging the terms, we get the equation like
$ \Rightarrow 5{x^2} - 8{x^2} + 7{x^2} - 7x + 2x - x + 3 - 5 - 2$
Now by using the BODMAS rule, we get the equation after adding will be equal to
$ \Rightarrow 4{x^2} - 6x - 4$
Therefore, we can say that on adding $5{x^2} - 7x + 3, - 8{x^2} + 2x - 5{\text{ and 7}}{{\text{x}}^2} - x - 2$ these terms we get $4{x^2} - 6x - 4$.

Hence, the option $\left( b \right)$ is correct.

Note:
This problem can also be solved in one more way or we can say that this method will look more amateur. In this, we will just take the terms like ${x^2}$common from the term in which this present and then similarly for the other two also and then we will solve them easily. I would suggest this method because it will be less confusing while solving so it minimizes the error.