Explain how to expand a single bracket.
E.g. .
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Explain how to expand a single bracket.
E.g. .
Expanding a bracket means multiplying the term outside the bracket by each term inside the bracket.
So becomes from .
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 an expression with two sets of brackets
E.g. .
To simplify expressions like you expand the brackets then collect like terms.
So expands to give .
The terms are then collected 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?
E.g. .
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 .
This can be found by multiplying outside the bracket by the highest power, , from inside the bracket.
When expanding double brackets, e.g. , what does the acronym FOIL stand for?
When expanding double brackets, e.g. , the acronym FOIL is used to identify which terms should be multiplied together.
F = First (the first term from each bracket, e.g. )
O = Outside (the outer term from each bracket, e.g. )
I = Inside (the inner term from each bracket, e.g. )
L = Last (the last term from each bracket, e.g. )
True or False?
When expanding double brackets such as , 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.
E.g. .
The double brackets can be expanded to .
What next step is required?
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 double brackets using the acronym FOIL, is it ok to rearrange the order, such as LIFO.
True.
When expanding double 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 an 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,
e.g..
Then expand the double brackets to get .
This then 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).
The expression can be written as .
What should be the next step, before expanding any more brackets?
The expression should be simplified by collecting like terms in the second bracket.
So becomes .
This reduces the next expansion from 8 calculations to 6 calculations!
True or False?
The term in the expansion of can be determined without expanding fully.
True.
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 an expression such as .
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.