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Method 1 (the distributive law)

\n

We expand $\\simplify{(x+{a[0]})(x-{a[0]})}$ one bracket at a time. 

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$\\simplify{(x+{a[0]})(x-{a[0]})}$$=$\n

$\\simplify{x(x-{a[0]})+{a[0]}(x-{a[0]})}$

\n		\n

          (each term in one bracket times the entire other bracket)

\n
$=$$\\simplify{x^2-{a[0]}x+{a[0]}x-{a[0]*a[0]}}$          (use the distributive law on each bracket)
$=$$\\simplify{x^2-{a[0]*a[0]}}$          (collect like terms)
\n

Method 2 (FOIL)

\n

Multiply the First terms in each bracket, then the Outer terms, then the Inner terms and then the Last terms. Add them all together.

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$\\simplify{(x+{a[0]})(x-{a[0]})}$$=$\n

$\\simplify[basic]{x^2-{a[0]}x+{a[0]}x-{a[0]*a[0]}}$

\n		\n

          (First, Outer, Inner, Last)

\n
$=$$\\simplify{x^2-{a[0]*a[0]}}$          (collect like terms)
\n

Method 3 (difference of two squares)

\n

Notice that the product will expand to be a difference of two squares. Square the first term minus the square of the second term. 

\n\n\n\n\n\n\n\n\n\n
$\\simplify{(x+{a[0]})(x-{a[0]})}$$=$\n

$\\simplify{x^2-{a[0]*a[0]}}$

\n		\n

          (difference of two squares)

\n
\n

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Ensure you don't use brackets in your answer.

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$\\simplify{(x+{a[0]})(x-{a[0]})}$ = [[0]]

\n

\n

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It is important to realise that $\\simplify{(x+{a[2]})^2}=\\simplify{(x+{a[2]})(x+{a[2]})}$. Recall that squaring something is multiplying it by itself.

\n

 

\n

Method 1 (the distributive law)

\n

We expand $\\simplify{(x+{a[2]})(x+{a[2]})}$ one bracket at a time. 

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$\\simplify{(x+{a[2]})(x+{a[2]})}$$=$\n

$\\simplify{x(x+{a[2]})+{a[2]}(x+{a[2]})}$

\n		\n

          (each term in one bracket times the entire other bracket)

\n
$=$$\\simplify{x^2+{a[2]}x+{a[2]}x+{a[2]*a[2]}}$          (use the distributive law on each bracket)
$=$$\\simplify{x^2+{2*a[2]}x+{a[2]*a[2]}}$          (collect like terms)
\n

Method 2 (FOIL)

\n

Multiply the First terms in each bracket, then the Outer terms, then the Inner terms and then the Last terms. Add them all together.

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$\\simplify{(x+{a[2]})(x+{a[2]})}$$=$\n

$\\simplify[basic]{x^2+{a[2]}x+{a[2]}x+{a[2]*a[2]}}$

\n		\n

          (First, Outer, Inner, Last)

\n
$=$$\\simplify{x^2+{2*a[2]}x+{a[2]*a[2]}}$          (collect like terms)
\n

Method 3 (perfect square)

\n

Notice that $\\simplify{(x+{a[2]})^2}$ is a perfect square. Square the first term, double the second term times the first, then square the last term, add them all together.

\n\n\n\n\n\n\n\n\n\n
$\\simplify{(x+{a[2]})}$$=$\n

$\\simplify{x^2+{2*a[2]}x+{a[2]*a[2]}}$

\n		\n

          (perfect square)

\n
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Ensure you don't use brackets in your answer.

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$\\simplify{(x+{a[2]})^2}$ = [[0]]

\n

\n

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Method 1 (the distributive law)

\n

We expand $\\simplify{(w+{a[1]})(w-{a[1]})}$ one bracket at a time. 

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$\\simplify{(w+{a[1]})(w-{a[1]})}$$=$\n

$\\simplify{w(w-{a[1]})+{a[1]}(w-{a[1]})}$

\n		\n

          (each term in one bracket times the entire other bracket)

\n
$=$$\\simplify{w^2-{a[1]}w+{a[1]}w-{a[1]*a[1]}}$          (use the distributive law on each bracket)
$=$$\\simplify{w^2-{a[1]*a[1]}}$          (collect like terms)
\n

Method 2 (FOIL)

\n

Multiply the First terms in each bracket, then the Outer terms, then the Inner terms and then the Last terms. Add them all together.

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$\\simplify{(w+{a[1]})(w-{a[1]})}$$=$\n

$\\simplify[basic]{w^2-{a[1]}w+{a[1]}w-{a[1]*a[1]}}$

\n		\n

          (First, Outer, Inner, Last)

\n
$=$$\\simplify{w^2-{a[1]*a[1]}}$          (collect like terms)
\n

Method 3 (difference of two squares)

\n

Notice that the product will expand to be a difference of two squares. Square the first term minus the square of the second term. 

\n\n\n\n\n\n\n\n\n\n
$\\simplify{(w+{a[1]})(w-{a[1]})}$$=$\n

$\\simplify{w^2-{a[1]*a[1]}}$

\n		\n

          (difference of two squares)

\n
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Ensure you don't use brackets in your answer.

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$\\simplify{(w+{a[1]})(w-{a[1]})}$ = [[0]]

\n

\n

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Method 1 (the distributive law)

\n

We expand $\\simplify{(r+{a[3]})(r+{a[3]})}$ one bracket at a time. 

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$\\simplify{(r+{a[3]})(r+{a[3]})}$$=$\n

$\\simplify{r(r+{a[3]})+{a[3]}(r+{a[3]})}$

\n		\n

          (each term in one bracket times the entire other bracket)

\n
$=$$\\simplify{r^2+{a[3]}r+{a[3]}r+{a[3]*a[3]}}$          (use the distributive law on each bracket)
$=$$\\simplify{r^2+{2*a[3]}r+{a[3]*a[3]}}$          (collect like terms)
\n

Method 2 (FOIL)

\n

Multiply the First terms in each bracket, then the Outer terms, then the Inner terms and then the Last terms. Add them all together.

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$\\simplify{(r+{a[3]})(r+{a[3]})}$$=$\n

$\\simplify[basic]{r^2+{a[3]}r+{a[3]}r+{a[3]*a[3]}}$

\n		\n

          (First, Outer, Inner, Last)

\n
$=$$\\simplify{r^2+{2*a[3]}r+{a[3]*a[3]}}$          (collect like terms)
\n

Method 3 (perfect square)

\n

Notice that $\\simplify{(r+{a[3]})(r+{a[3]})}$ is a perfect square. Square the first term, double the second term times the first, then square the last term, add them all together.

\n\n\n\n\n\n\n\n\n\n
$\\simplify{(r+{a[3]})(r+{a[3]})}$$=$\n

$\\simplify{r^2+{2*a[3]}r+{a[3]*a[3]}}$

\n		\n

          (perfect square)

\n
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Ensure you don't use brackets in your answer.

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$\\simplify{(r+{a[3]})(r+{a[3]})}$ = [[0]]

\n

\n

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Expand and simplify the following.

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