Expanding 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:

 3(x+6)=3×x+3×6=3x+18  .

b) Expand:  6(4a−10).

b) Remember to multiply every term inside the brackets by the term outside:

6(4a−10)=24a−60.

c) Expand: 3xy(2x+y2).

c) When multiplying more complicated terms, multiply the numbers first followed by the letters:

3xy(2x+y2)=6x2y+3xy3.

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:

2(3x+4)+4(x−1)=6x+8+4x−4=10x+4

b) Expand and simplify 7(3n−9)−4(6−4n).

Be very careful when multiplying out brackets with lots of negative signs:

7(3n−9)−4(6−4n)=21n−63−24+16n=37n−87

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:

(a+b)(c+d)=ac+ad+bc+bd.

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