Expanding brackets with surds

When expanding brackets that contain surds, we use the same methods as we do with normal brackets, (e.g. the grid method).

We just need to remember how to multiply surds together.

Example: Expand

Draw a grid with two rows and two columns, since we have two terms in each set of brackets:

Multiply the terms:

Remember that when multiplying two of the same surds together (e.g ), the result is the number inside the surd (in this case, ).

Add the terms in the middle of the grid together to get the final answer:

• - add the whole number parts as the surd parts are the same.
• Answer:

Example: Expand

Draw a grid with two rows and two columns, since we have two terms in each set of brackets:

Multiply the terms:

Add the terms in the middle of the grid together to get the final answer:

• - add the whole number parts as the surd parts are the same.

Answer: