Algebra

Question 1

Distributive law

Answer 1

• When a coefficient is multiplied by a bracket containing two terms, the coefficient multiplies against both terms
• Often known as the “rainbow method
• a(b+c) = ab + ac

Question 2

Rules of multiplying and dividing integers

Answer 2

Positive x positive = +
Negative x negative = +
Positive x negative = -
Negative x positive = -

Question 3

Product law

Answer 3

Also known as Expansion of Squares or FOIL
- F = First
- O = Outside
- I = Inner
- L = last
(a + b) (c + d) = (ac + ad + bc + bd)

Question 4

Difference of Squares

Answer 4

FOIL
- F = First
- O = Outside
- I = Inner
- L = last
(a + b) (a - b) = a^2 - b^2

Question 5

Perfect squares expansion

Answer 5

FOIL
- F = First
- O = Outside
- I = Inner
- L = last
(a + b) (a + b) = a^2 + 2ab + b^2

Question 6

Further Expansion

Trinomials

Expanding with 3 brackets

Answer 6

• Disributive Law can apply to more than two terms
• Each term in 1st bracket is multiplied by each term in 2nd one

If you have a trinomial multiplied by another trinomial: same rules apply

If you have 3 brackets: simplify expression by expanding 2 brackets first

Question 7

Reverse Distributive Law

Answer 7

Factorization:
- The process of writing an expression as a product of its factors

How we do it:
- To factorize an algebraic expression with a number of terms, we find the HCF of all the terms and write it separately as a new
coefficient in front of a set of brackets.

• HCF = Highest Common Factor
• We find the new content of the brackets

Question 8

Factoring with 4 terms

Answer 8

• Some expressions with four terms do not have an overall common factor but can be factorized by grouping

Steps:
1. Pair together the four terms into two sets of two with recognizable common factors
2. Factor out the common factors for each pair as coefficient
3. What has been factored out will then be common, and can be factored out to be the first bracket, and the second bracket will be the coefficients.

Question 9

Factoring trinomials

Answer 9

Split the three terms into four by:

• finding the numbers that get a product of the constant term, and sum to the coefficient of the variable
• then, split the coefficient up into the two numbers (a and b)
• make a bracket with (x + a) + (x + b)

*Occasionally you need to factor out a common factor first, which remains as a coefficient

Question 10

Trinomials where coefficient of x^2 doesn’t equal 1

Answer 10

• There will be questions when ‘a’ doesn’t equal 1 in which we cannot remove a common factor

In order for us to solve this, we need to “split” the middle term

ax^2 +bx + c

• Step 1: Find two numbers who sum make b and whose product is ac
• Step 2: Replace bx with those two numbers
• Step 3: Complete the Factorization by ‘grouping’