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Regn ut og gjør uttrykkene eklere.

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Bruk ^ for å skrive en potens, f.eks skriver du a^3 for å få \$a^3\$

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Method 1 (the distributive law)

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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)
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Method 2 (FOIL)

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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)
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Method 3 (difference of two squares)

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

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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.

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Method 1 (the distributive law)

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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)
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Method 2 (FOIL)

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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)
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Method 3 (perfect square)

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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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