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Expanding brackets means multiplying everything inside the bracket by the letter or number outside the bracket. For example, in the expression \(3(m + 7)\) both \(m\) and 7 must be multiplied by 3:

\(3(m + 7) = 3 \times m + 3 \times 7 = 3m + 21\).

Expanding brackets involves using the skills of simplifying algebra. Remember that \(2 \times a = 2a\) and \(a \times a = a^2\).

Expand \(4(3n + y)\).

\(4(3n + y) = 4 \times 3n + 4 \times y = 12n + 4y\)

Powers or index numbers are the floating numbers next to terms that show how many times a letter or number has been multiplied by itself. For example, \(a^2 = a \times a\) and \(a^4 = a \times a \times a \times a\).

Using index laws, terms that contain powers can be simplified. Remember that multiplying indices means adding the powers. For example, \(a^2 \times a^3 = (a \times a) \times (a \times a \times a) = a^5\).

Expand the bracket \(3b^2(2b^3 + 3b)\).

Multiply \(3b^2\) by \(2b^3\) first. \(3 \times 2 = 6\) and \(b^2 \times b^3 = b^5\), so \(3b^2 \times 2b^3 = 6b^5\).

Then multiply \(3b^2\) by \(3b\). \(3 \times 3 = 9\) and \(b^2 \times b = b^3\), so \(3b^2 \times 3b = 9b^3\).

So, \(3b^2(2b^3 + 3b) = 6b^5 + 9b^3\).

Expressions with brackets can often be mixed in with other terms. For example, \(3(h + 2) - 4\). In these cases first expand the bracket and then collect any like terms.

Expand and simplify \(3(h + 2) - 4\).

\(3(h + 2) - 4 = 3 \times h + 3 \times 2 - 4 = 3h + 6 - 4 = 3h + 2\)

Expand and simplify \(6g + 2g(3g + 7)\).

This gives: \(6g + 2g(3g + 7) = 6g + 2g \times 3g + 2g \times 7 = 6g + 6g^2 + 14g\)

Collecting the like terms gives \(6g^2 + 20g\).