Removing brackets is to multiply the term outside the brackets by each term inside - also known as the distributive law. Use FOIL to remove a pair of brackets then simplify by collecting like terms.

Part of

To remove brackets, multiply the term on the outside of the bracket with each term inside the brackets.

This process to remove brackets is also known as the **distributive law**.

Look at the National 4 distributive law chapter before continuing.

Here, we combine multiplying out brackets and collecting like terms, to simplify algebraic expressions.

Have a look at the example questions below.

- Question
Expand and simplify:

\[3(x + y) + 2(x + y)\]

\[= 3x + 3y + 2x + 2y\]

\[= 5x + 5y\]

- Question
Expand and simplify:

\[4(2p + 7) + 6(8q - 2)\]

\[= 8p + 28 + 48q - 12\]

\[= 8p + 48q + 16\]

- Question
Expand and simplify:

\[9(2x + 3) - 3(5x + 1)\]

\[= 18x + 27 - 15x - 3\]

\[= 3x + 24\]

- Question
Expand and simplify:

\[5(3p+2) -2 (4q+3)\]

\[=15p+10-8q-6\]

\[=15p-8q+4\]

Remove the brackets for the expression:

\[4x(x + 5)\]

This expression means everything inside the brackets is multiplied by \(4x\).

\[= (4x \times x) + (4x \times 5)\]

\[= 4{x^2} + 20x\]

Multiply out the brackets in \(3a(2a + 1)\):

\[= (3a \times 2a) + (3a \times 1)\]

\[= 6{a^2} + 3a\]

Now try the example questions below.

- Question
Multiply out the brackets in \(5y(3 - y)\)

\[= 15y - 5{y^2}\]

- Question
Remove the brackets from \(4w(3w - 2y)\)

\[= (4w \times 3w) - (4w \times 2y)\]

\[= 12{w^2} - 8wy\]