Removing brackets

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:

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

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

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

Examples with an x-coefficient

Step one

Remove the brackets for the expression:

\[4x(x + 5)\]

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

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

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

Step two

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 \(4w(3w - 2y)\)

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

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