Expanding double brackets

Writing two brackets next to each other means the brackets need to be multiplied together. For example, \((y + 2)(y + 3)\) means \((y + 2) \times (y + 3)\).

When expanding double brackets, every in the first bracket has to be multiplied by every term in the second bracket. It is helpful to always multiply the terms in order so none are forgotten. One common method used is FOIL: First, Outer, Inside, Last.

Example

Expand the brackets \((y + 2)(y + 3)\).

Multiply the first items in the brackets: \(y \times y = y^2\)

Multiply the outer terms of the brackets: \(y \times 3 = 3y\)

Multiply the inner terms of the brackets: \(2 \times y = 2y\)

Multiply the last terms in the brackets: \(2 \times 3 = 6\)

This gives: \(y^2 + 3y + 2y + 6\)

Simplify the like terms \((3y + 2y)\) to give \(y^2 + 5y + 6\).

Question

Expand the bracket \((2m - 3)(m + 1)\).

Another method for multiplying brackets is to use a grid.

To expand the bracket \((m + 1)(2m - 3)\) :

A grid that has expanded the bracket (2m – 3) (m+1)

So \((m + 1)(2m-3) = 2m^2 - 3m + 2m - 3 = 2m^2-m-3\)

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Algebraic expressions - AQAExpanding double brackets