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
