Explain how to expand a single bracket, such as .
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Explain how to expand a single bracket, such as .
Expanding a bracket means multiplying the term outside the bracket by each term inside the bracket.
So becomes from .
Does expanding brackets work with different letters inside the brackets, such as ?
Yes, expanding brackets works with different letters inside the brackets.
So expands to give .
Does expanding brackets work when there is a negative number on the outside?
Yes, expanding brackets works when there is a negative number on the outside. You need to be very careful with signs though, as and .
For example, expands to give .
True or False?
expands to .
False.
can be thought of as . Multiplying two negatives gives a positive, so the answer is .
How can you simplify before expanding the brackets?
You can simplify before expanding by first collecting like terms inside the brackets to give . This can also be written as .
Explain how to simplify expressions like .
To simplify expressions like you expand the brackets then collect like terms.
So expands to give , the the terms are collected to give .
Does expanding brackets work when the term outside the bracket has letters in it, like ?
Yes, expanding brackets works when the term outside has letters in it. You also need to remember index rules such as .
So expands to give .
True or False?
expands to , then the 3's cancel to give .
False.
You cannot cancel the 3's because is an expression, not an equation.
You can only cancel both sides by 3 if you had an equation, like .
How do you find the highest power of when expanding expressions like ?
The highest power of will come from multiplying the outside term by the inside term with the highest power.
The highest power of in is by multiplying outside the bracket by the highest power, , from inside the bracket.
Write down the four words represented by the acronym FOIL when expanding double brackets.
F = First
O = Outside (or outer)
I = Inside (or inner)
L = Last
When expanding , what is the term given by the O in the acronym FOIL?
When expanding , the O in FOIL means multiply the outer terms in the brackets (the one farthest on the left by the one farthest on the right).
This is giving .
True or False?
When expanding double brackets like , every term in the left bracket gets multiplied by every term in the right bracket.
True.
When expanding double brackets like , every term in the left bracket gets multiplied by every term in the right bracket.
When expanding , a student correctly gets .
What step should they do next?
The next correct step is to simplify the expression by collecting like terms.
So becomes . You cannot simplify it any further.
True or False?
When expanding brackets using the acronym FOIL, is it ok to rearrange the order, such as LIFO.
True.
When expanding brackets using the acronym FOIL, is it ok to rearrange the order, such as LIFO.
When you collect terms at the end, you will have a expression that is mathematically the same as using FOIL.
True or False?
.
False.
To square a single bracket, you first need to write it as double brackets.
, then expand the double brackets to get which simplifies to .
The incorrect answer of is missing the middle term, .
True or False?
When expanding , you can choose which pair of brackets to multiply out first (the order does not matter).
True.
When expanding , you can choose which pair of brackets to multiply out first (the order does not matter).
In the expansion of , a student correctly gets .
What should the student do next, before expanding any more brackets?
The student should simplify the second bracket by collecting like terms.
So becomes .
This reduces their next expansion from 8 calculations to 6 calculations!
How can you see that the term in the expansion of will be , without expanding fully?
You can see that the term in the expansion of will be by:
Writing the brackets in order,
Multiplying the terms together,
This gives , without needing to expand fully.
Explain the process for expanding something like .
To expand , you need to:
Write it as a triple bracket expansion,
Pick two brackets and expand and simplify them
Expand this result with the remaining bracket
Simplify the final answer by collecting like terms