Question

Combine like terms11) x^2 + 3x - 5 + x^2 - 2x - 5

Answer 1

Like terms are those terms whose variables are the same, and those variables appear with the same exponents.

In the given expression:

$x^2+3x-5+x^2-2x-5$

There are 6 terms in total. Notice that there are two quadratic terms:

$x^2\text{ and }x^2$

There are two linear terms:

$3x\text{ and }-2x$

And there are two constant terms:

$-5\text{ and }-5$

To combine like terms, add their coefficients. If a term does not have an explicit coefficient, it is equal to 1.

Then:

$\begin{gathered} x^2+x^2=2x^2 \\ 3x-2x=x \\ -5-5=-10 \end{gathered}$

Therefore:

$x^2+3x-5+x^2-2x-5=2x^2+x-10$