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Expanding Brackets (Edexcel GCSE Maths: Foundation): Flashcards

Exam code: 1MA1

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FrontExpanding & Simplifying Single Brackets
Explain how to expand a single bracket.
E.g. $2 (x + 3)$ .

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Cards in this collection (11)

Explain how to expand a single bracket.
E.g. $2 (x + 3)$ .
Expanding a bracket means multiplying the term outside the bracket by each term inside the bracket.
So $2 (x + 3)$ becomes $2 x + 6$ from $2 \times x + 2 \times 3$ .
True or False?
$- 2 (1 - x)$ expands to $- 2 - 2 x$ .
False.
$- 2 (1 - x)$ can be thought of as $(- 2) \times 1 + (- 2) \times (- x)$ .
Multiplying two negatives gives a positive, so the answer is $- 2 + 2 x$ .
How can you simplify $3 (x + 5 + x)$ before expanding the brackets?
You can simplify $3 (x + 5 + x)$ before expanding by first collecting like terms inside the brackets to give $3 (2 x + 5)$ .
This can also be written as $3 (5 + 2 x)$ .
Explain how to simplify an expression with two sets of brackets
E.g. $2 (x + 1) + 3 (x - 1)$ .
To simplify expressions like $2 (x + 1) + 3 (x - 1)$ you expand the brackets then collect like terms.
So $2 (x + 1) + 3 (x - 1)$ expands to give $2 x + 2 + 3 x - 3$ .
The terms are then collected to give $5 x - 1$ .
True or False?
$3 (x + 2)$ expands to $3 x + 6$ , then the 3's cancel to give $x + 2$ .
False.
You cannot cancel the 3's because $3 (x + 2)$ is an expression, not an equation.
You can only cancel both sides by 3 if you had an equation, like $3 (x + 2) = 9$ .
How do you find the highest power of $x$ when expanding expressions?
E.g. $2 x^{2} (x + x^{2})$ .
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 $2 x^{2} (x + x^{2})$ is $x^{4}$ .
This can be found by multiplying $x^{2}$ outside the bracket by the highest power, $x^{2}$ , from inside the bracket.
How many multiplications are needed to expand $(x + 1) (x + 3)$ , and why?
Four, because every term in the first bracket must be multiplied by every term in the second bracket.
The four products here are $x \times x$ , $x \times 3$ , $1 \times x$ and $1 \times 3$ .
Complete the expansion by filling in the missing numbers:
$(2 x - 3) (x + 4) = 2 x^{2} +______x -______$
The completed expansion is:
$(2 x - 3) (x + 4) = 2 x^{2} + 5 x - 12$
The two middle products, $8 x$ and $- 3 x$ , are like terms, so they combine into the single term $5 x$ .
When expanding $(x - 3) (3 x - 5)$ using FOIL, which two products are the Outside and Inside ones?
Outside is $x \times (- 5)$ , the first term of the first bracket multiplied by the last term of the second bracket.
Inside is $(- 3) \times 3 x$ , the last term of the first bracket multiplied by the first term of the second bracket.
True or False?
${(x + y)}^{2}$ expands to $x^{2} + y^{2}$ .
False.
The expansion of ${(x + y)}^{2}$ is $x^{2} + x y + x y + y^{2}$ , which simplifies to $x^{2} + 2 x y + y^{2}$ .
The two $x y$ cross terms are exactly what $x^{2} + y^{2}$ leaves out.
What is the first thing to do when expanding ${(x + 3)}^{2}$ ?
Write the square as two brackets multiplied together, $(x + 3) (x + 3)$ .
It can then be expanded in exactly the same way as any other pair of brackets.

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