GCSE(F), GCSE(H),

Multiplying out brackets is **expanding** an expression.

For example: expand 3*a*(4*a* - 3*b* + 6). Set out the terms within the brackets as a list, deal with them individually, then add them together:

4*a* x 3*a* = 12*a*^{2}

-3*b* x 3*a* = -9*ab*

6 x 3*a* = 18*a*

Note that *every* term in the bracket is multiplied by the term outside the bracket, and that negative signs are taken into account. Put the answer together:

3*a*(4*a* - 3*b* + 6) = 12*a*^{2} - 9*ab* + 18*a*

1. Expand and simplify 3(*m* + 2) + 4*m*.

Answer: 7*m* + 6

Expand the bracket:

*m* x 3 = 3*m*

2 x 3 = 6

Put it all together. Include the 4*m* that was outside the bracket:

3*m* + 6 + 4*m* = 7*m* + 6

2. Expand and simplify: 6 - *a*(*a* - 2).

Answer: -*a*^{2} + 2*a* + 6

Expand the brackets, taking very careful note of the negative signs:

*a* x -*a* = -*a*^{2}

-2 x -*a* = 2*a*

Putting it all together, with the leading 6:

-*a*^{2} + 2*a* + 6

It is normal to put a list of terms in descending order of their powers.

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