This document discusses factorizing algebraic expressions by taking out common factors. It begins by recapping the process of expanding brackets by multiplying each term inside the brackets by each term outside. It then explains that factorizing is the reverse of this, involving taking out any common factors. As an example, it shows factorizing x2 + x as x(x + 1) since x is a common factor. The document concludes by providing 4 examples of expressions to factorize.

1. FACTORING/FACTORISATION

2. EXPANDING BRACKETS RECAP
• Remember in week 3 of term 1 when we looked at laws of exponents we
touched on the concept of expanding brackets.
• If we have an expression like y(2 + 3) and we are required to expand the
brackets, we would simply multiply the term outside the bracket by each and
every term inside the bracket.
• Thus for y(2 + 3) you would expand by multiplying y by 2 and add to the
product of y multiplied by 3….. yx2 + yx3 = 2y +3y
• For an expression like z(2z – 3y) you would multiply z by 2z and add to z
multiplied by -3y
thus, zx2z + zx-3y = 2z2 + 3yz
• For an expression like (2y + y)(z + 3z) you multiply each and every term in the
first bracket by each and every term in the second bracket as follows:
2y(z + 3z) + y(z + 3z) = 2yz + 6yz + yz +3yz

3. • Now we must understand that factorisation is the reverse
of expanding brackets.
• The first step of factorising an expression is to 'take out'
any common factors which the terms have. So if you were
asked to factorise
x² + x, since x goes into both terms, you would write x(x
+ 1) .
• For the expression 3x – 6 , the common factor that can
divide into both 3x and 6 is 3 so we take 3 outside the
bracket as follows:
3(x – 2).

4. •Now try and factorise the
following:
1.x3 + 3x2
2.2y – 6zy
3.2z3 + 4z
4.3x4 – 9x3y