Expanding a single pair of brackets
Example 1 - Expanding a single pair of brackets
a) Expand: 3(x+6) .
a) Remember to multiply every term inside the brackets by the term outside:
b) Expand: 6(4a−10).
b) Remember to multiply every term inside the brackets by the term outside:
c) Expand: 3xy(2x+y2).
c) When multiplying more complicated terms, multiply the numbers first followed by the letters:
Expanding and simplifying brackets
Example 2 - Expanding and simplifying brackets
a) Expand and simplify 2(3x+4)+4(x−1).
Multiply each bracket out first, then collect the like terms:
b) Expand and simplify 7(3n−9)−4(6−4n).
Be very careful when multiplying out brackets with lots of negative signs:
Expanding double brackets
Example 3 - Expanding double brackets
Expand and simplify (a+b)(c+d).
When multiplying out double brackets, each terms in the first bracket must be multiplied by each term in the second:
Expandin and simplifying quadratic expressions
Example 4 - Expanding and simplifying quadratic expressions
a) Expand and simplify (x+4)(x+3).
When multiplying x by another x you will end up with an x2 term:
(x+4)(x+3 )= x2+3x+4x+12 = x2+7x+12
b) Expand and simplify (3x−10)(5x−9).
Remember, when multiplying two negative terms you will get a positive:
(3x−10)(5x−9) = 15x2−27x−50x+90 = 15x2−77x+90