How to expand brackets?

Expand 5(x - 4)

To expand the brackets, you must mutilpy the number outside the bracket by everything inside.

Step 1)  5 x x  =  5x

Step 2)  5 x (-4)  =  -20     Remember to include the minus sign

Adding the answers together, we get 5x - 20

 

The same method applies if there is a letter outside the brackets instead of a number.

Expand y(x + 3) 

Step 1)  y x x  =  xy

Step 2)  y x 3  =  3y

 

So y(x + 3)  =  xy +3y

 

Expand (x + 2)(y + 5)

 

To expand two sets of brackets, you need to multiply every term in the first bracket by every term in the second bracket. For example, multiply everything in the second bracket by x and then by 2:

Step 1)   x x y  =  xy

Step 2)   x x 5  =  5x

Step 3)   2 x y  =  2y

Step 4)   2 x 5  =  10

Now add the answers to the 4 steps together:

xy + 5x + 2y + 10

 

Expand (a - 4)(b - 1)

 

Step 1)  a x b  =  ab

Step 2)  a x (-1) =  -a    Again, remember to incude the minus sign

Step 3)  (-4) x b  =  -4b

Step 4)  (-4) x (-1)  =  4

Together: ab - a - 4b+ 4

 

Exercises:

Expand all these brackets

 

3(d + 9)

2(8 + d)

z(2 - k)

-f(3 + h)

 

(c + 6)(d+ 2)

(s - 7)(t+ 9)

( u + v)(w - g)