IGCSEMaths A: HigherEdexcelFlashcards

Expanding Brackets (Edexcel IGCSE Maths A)

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  • Explain how to expand a single bracket, such as 2 open parentheses x plus 3 close parentheses.

    Expanding a bracket means multiplying the term outside the bracket by each term inside the bracket.

    So 2 open parentheses x plus 3 close parentheses becomes 2 x plus 6 from 2 cross times x plus 2 cross times 3.

  • Does expanding brackets work with different letters inside the brackets, such as 5 open parentheses x plus y close parentheses?

    Yes, expanding brackets works with different letters inside the brackets.

    So 5 open parentheses x plus y close parentheses expands to give 5 x plus 5 y.

  • 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 plus cross times negative equals negative and negative cross times negative equals plus.

    For example, negative 5 open parentheses x plus 1 close parentheses expands to give negative 5 x minus 5.

  • True or False?

    negative 2 open parentheses 1 minus x close parentheses expands to negative 2 minus 2 x.

    False.

    negative 2 open parentheses 1 minus x close parentheses can be thought of as open parentheses negative 2 close parentheses cross times 1 plus open parentheses negative 2 close parentheses cross times open parentheses negative x close parentheses. Multiplying two negatives gives a positive, so the answer is negative 2 plus 2 x.

  • How can you simplify 3 open parentheses x plus 5 plus x close parentheses before expanding the brackets?

    You can simplify 3 open parentheses x plus 5 plus x close parentheses before expanding by first collecting like terms inside the brackets to give 3 open parentheses 2 x plus 5 close parentheses. This can also be written as 3 open parentheses 5 plus 2 x close parentheses.

  • Explain how to simplify expressions like 2 open parentheses x plus 1 close parentheses plus 3 open parentheses x minus 1 close parentheses.

    To simplify expressions like 2 open parentheses x plus 1 close parentheses plus 3 open parentheses x minus 1 close parentheses you expand the brackets then collect like terms.

    So 2 open parentheses x plus 1 close parentheses plus 3 open parentheses x minus 1 close parentheses expands to give 2 x plus 2 plus 3 x minus 3, the the terms are collected to give 5 x minus 1.

  • Does expanding brackets work when the term outside the bracket has letters in it, like 4 x open parentheses x plus 1 close parentheses?

    Yes, expanding brackets works when the term outside has letters in it. You also need to remember index rules such as x cross times x equals x squared.

    So 4 x open parentheses x plus 1 close parentheses expands to give 4 x squared plus 4 x.

  • True or False?

    3 open parentheses x plus 2 close parentheses expands to 3 x plus 6, then the 3's cancel to give x plus 2.

    False.

    You cannot cancel the 3's because 3 open parentheses x plus 2 close parentheses is an expression, not an equation.

    You can only cancel both sides by 3 if you had an equation, like 3 open parentheses x plus 2 close parentheses equals 9.

  • How do you find the highest power of x when expanding expressions like 2 x squared open parentheses x plus x squared close parentheses?

    The highest power of x will come from multiplying the outside term by the inside term with the highest power.

    The highest power of x in 2 x squared open parentheses x plus x squared close parentheses is x to the power of 4 by multiplying x squared outside the bracket by the highest power, x squared, 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 open parentheses x plus 1 close parentheses open parentheses x plus 2 close parentheses, what is the term given by the O in the acronym FOIL?

    When expanding open parentheses x plus 1 close parentheses open parentheses x plus 2 close parentheses, 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 x cross times 2 giving 2 x.

  • True or False?

    When expanding double brackets like open parentheses x plus 1 close parentheses open parentheses x plus 2 close parentheses, every term in the left bracket gets multiplied by every term in the right bracket.

    True.

    When expanding double brackets like open parentheses x plus 1 close parentheses open parentheses x plus 2 close parentheses, every term in the left bracket gets multiplied by every term in the right bracket.

  • When expanding open parentheses x plus 1 close parentheses open parentheses x plus 2 close parentheses, a student correctly gets x squared plus 2 x plus x plus 2.

    What step should they do next?

    The next correct step is to simplify the expression by collecting like terms.

    So x squared plus 2 x plus x plus 2 becomes x squared plus 3 x plus 2. 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?

    open parentheses x plus 5 close parentheses squared equals x squared plus 25.

    False.

    To square a single bracket, you first need to write it as double brackets.

    open parentheses x plus 5 close parentheses squared equals open parentheses x plus 5 close parentheses open parentheses x plus 5 close parentheses, then expand the double brackets to get x squared plus 5 x plus 5 x plus 25 which simplifies to x squared plus 10 x plus 25.

    The incorrect answer of x squared plus 25 is missing the middle term, 10 x.

  • True or False?

    When expanding open parentheses x plus 1 close parentheses open parentheses x plus 2 close parentheses open parentheses x plus 3 close parentheses, you can choose which pair of brackets to multiply out first (the order does not matter).

    True.

    When expanding open parentheses x plus 1 close parentheses open parentheses x plus 2 close parentheses open parentheses x plus 3 close parentheses, you can choose which pair of brackets to multiply out first (the order does not matter).

  • In the expansion of open parentheses x plus 1 close parentheses open parentheses x plus 2 close parentheses open parentheses x plus 3 close parentheses, a student correctly gets open parentheses x plus 1 close parentheses open parentheses x squared plus 3 x plus 2 x plus 6 close parentheses.

    What should the student do next, before expanding any more brackets?

    The student should simplify the second bracket by collecting like terms.

    So open parentheses x plus 1 close parentheses open parentheses x squared plus 3 x plus 2 x plus 6 close parentheses becomes open parentheses x plus 1 close parentheses open parentheses x squared plus 5 x plus 6 close parentheses.

    This reduces their next expansion from 8 calculations to 6 calculations!

  • How can you see that the x cubed term in the expansion of open parentheses x plus 1 close parentheses open parentheses 2 x plus 1 close parentheses open parentheses 1 plus 3 x close parentheses will be 6 x cubed, without expanding fully?

    You can see that the x cubed term in the expansion of open parentheses x plus 1 close parentheses open parentheses 2 x plus 1 close parentheses open parentheses 1 plus 3 x close parentheses will be 6 x cubed by:

    1. Writing the brackets in order, open parentheses x plus 1 close parentheses open parentheses 2 x plus 1 close parentheses open parentheses 3 x plus 1 close parentheses

    2. Multiplying the x terms together, x cross times 2 x cross times 3 x

    This gives 6 x cubed, without needing to expand fully.

  • Explain the process for expanding something like open parentheses x minus 2 close parentheses cubed.

    To expand open parentheses x minus 2 close parentheses cubed, you need to:

    1. Write it as a triple bracket expansion, open parentheses x minus 2 close parentheses open parentheses x minus 2 close parentheses open parentheses x minus 2 close parentheses

    2. Pick two brackets and expand and simplify them

    3. Expand this result with the remaining bracket

    4. Simplify the final answer by collecting like terms

1. Numbers & the Number System
2. Equations, Formulae & Identities
3. Sequences, Functions & Graphs
4. Geometry & Trigonometry
5. Vectors & Transformation Geometry
6. Statistics & Probability