Expanding three brackets - using arrows
Expand two brackets first, then multiply the resulting polynomial by the third.
- Expand the first two brackets, then bring the third bracket to the front.
- Follow the blue arrows from the first term, then the green arrows from the second term.
- Write the products in two rows, lining up terms with the same power of
. - Add down each column, keeping the positive or negative sign with every term.
Example 1
Expand and simplify.
1. Expand the first two brackets.
2. Bring the third bracket to the front.
Example 2
Multiply out all three brackets and collect like terms.
1. Expand the first two brackets.
2. Bring the third bracket to the front.
Remember
The colours link each circled term to its row of products. Blank spaces keep matching powers aligned; only like terms can be added.
Your turn
Expand and simplify.
Check answer
1. Expand the first two brackets.
2. Bring the third bracket to the front.
Expand and simplify.
Check answer
1. Expand the first two brackets.
2. Bring the third bracket to the front.
Keep
Expand and simplify.
Check answer
1. Expand the first two brackets.
2. Bring the third bracket to the front.
Expand and simplify.
Check answer
1. Expand the first two brackets.
2. Bring the third bracket to the front.
Expand and simplify.
Check answer
Write the power as three factors.
1. Expand the first two brackets.
2. Bring the third bracket to the front.
Expand and simplify.
1. Expand the first two brackets.
2. Bring the third bracket to the front.
Expand and simplify.
1. Expand the first two brackets.
2. Bring the third bracket to the front.
Keep
Expand and simplify.
1. Expand the first two brackets.
2. Bring the third bracket to the front.
Expand and simplify.
1. Expand the first two brackets.
2. Bring the third bracket to the front.
Expand and simplify.
Write the power as three factors.
1. Expand the first two brackets.
2. Bring the third bracket to the front.