Question

The sum or difference of two like terms is ……………

Answer 1

Step 1: Find the sum of two like terms

We know that like terms are those terms that contain the same variable which is raised to the same power.

Now consider two like terms $8{\mathrm{x}}^2\mathrm{y}$ and $2{\mathrm{x}}^2\mathrm{y}$.

The sum of $8{\mathrm{x}}^2\mathrm{y}$ and $2{\mathrm{x}}^2\mathrm{y}$ $=8{\mathrm{x}}^2\mathrm{y}+2{\mathrm{x}}^2\mathrm{y}=10{\mathrm{x}}^2\mathrm{y}$, which is a like term.

Thus the sum of two like terms gives a like term.

Step 2: Find the difference of two like terms

Difference between $8{\mathrm{x}}^2\mathrm{y}$ and $2{\mathrm{x}}^2\mathrm{y}$ $=8{\mathrm{x}}^2\mathrm{y}-2{\mathrm{x}}^2\mathrm{y}=6{\mathrm{x}}^2\mathrm{y}$, which is a like term.

Thus the difference between two like terms gives a like term.

Therefore, the sum or difference of two like terms is also a like term.