Algebra

Question 1

Multiplying Out Double Brackets:

Answer 1

Every term in the first bracket has to be multiplied by every term in the second bracket.

e.g. (2x - 4)(x + 7),
=> 2x(x - 7) - 4(x + )
=> 2x(x) - 7(2x) - 4(x) - 4(7)
=> 2x{2} - 14x - 4x - 28
=> 2x{2} - 18x + 28

Question 2

Factorising the ‘‘Common Factor’’

Answer 2

Simplify expression by the HCF found (usually found in the first [biggest] figure and fits into each).

e.g. 15xy - 6x{2}y
=> 3xy(5 - 2x)
HCF -> 3xy

Question 3

Factorising the ‘‘Difference of Two Squares’’

Answer 3

1: Find HCF that fits into both figures.
2: Separate equation into 2 brackets.

e.g. 81 - y{2}
=> (9 + y)(9 - y)
or
d - 4d{2}
=> d(1 - 4d{2}
=> d(1 + 2d)(1 - 2d)

Question 4

Factorising Trinomials (Quadratic Expressions)

Answer 4

1: Find factors of the number term times by squared term (usually the first x last), use numbers which add to give you the middle number.
2: Find HCF of two x terms (usually first and second middle term).
3: Two brackets will be identical, place one down for final answer then use the last terms to make up the second bracket.

e.g. 3x{2} - 11x - 4
=> 3x{2} + x - 12x - 4
=> x(3x{2} + 1) - 4(3x + 1)
=>(x - 4)(3x + 1)
-> -11: -1 + 12, -12 + 1

Question 5

Simplifying Algebraic Fractions