**Every term**in the first bracket must be multiplied by**every term**in the second bracket- To expand (
*x*+ 1)(*x*+ 3) will need 4 multiplications in total

- To expand (
- A good way to remember all the multiplications is FOIL
- F =
**First**: multiply together the first terms in each bracket - O =
**Outside**: multiply the first term in the first bracket by the second term in the second bracket (visually, these are the "outer" terms) - I =
**Inside**: multiply the second term in the first bracket by the first term in the second bracket (visually, these are the "inner" terms) -
L =

**Last**: multiply together the last terms in each bracket

- F =
- It helps to put negative terms in brackets when multiplying
**Simplify**the final answer by**collecting like terms**(if there are any)

- To expand (
*x*+ 1)(*x*+ 3), write out the brackets as**headings**in a grid (in either direction) -
**x****+1****x****+3** - For each cell in the middle,
**multiply**the term in the**row**heading by the term in the**column**heading -
**x****+1****x***x*^{2}*x***+3**3 *x*3 **Add**together all the terms**inside**the grid to get the answer*x*^{2}+*x*+ 3*x*+ 3- collect like terms
*x*^{2}+ 4*x*+ 3

- Write (
*x*+ 3)^{2}as (*x*+ 3)(*x*+ 3) and use one of the methods above- for example, with FOIL: (
*x*+ 3)(*x*+ 3) =*x*^{2}+ 3*x*+ 3*x*+ 9 - collect like terms to get the final answer
*x*^{2}+ 6*x*+ 9

- for example, with FOIL: (
- Do
**not**make the common**mistake**of saying (*x*+ 3)^{2}is*x*^{2}+ 3^{2}- This cannot be true, as substituting
*x*= 1, for example, gives (1 + 3)^{2}= 4^{2}= 16 on the left, but 1^{2}+ 3^{2}= 1 + 9 = 10 on the right

- This cannot be true, as substituting

(a)

Expand .

Start by expanding the first two sets of brackets using the FOIL method and simplify by collecting 'like' terms.

Rewrite the original expression with the first two brackets expanded.

Multiply all of the terms in the first set of brackets by all of the terms in the second set of brackets.

Simplify.

Collect 'like' terms.

(b)

Expand .

Start by expanding the first two sets of brackets using the FOIL method and simplify by collecting 'like' terms.

Rewrite the original expression with the first two brackets expanded.

Multiply all of the terms in the first set of brackets by all of the terms in the second set of brackets.

Simplify.

Collect 'like' terms.

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