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$\\simplify[basic]{({c[0]}x+{a[0]})({d[0]}x+{b[0]})}$ = [[0]]

\n

\n

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Ensure you don't use brackets in your answer.

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Method 1 (the distributive law)

\n

We expand $\\simplify[basic]{({c[0]}x+{a[0]})({d[0]}x+{b[0]})}$ 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[basic]{({c[0]}x+{a[0]})({d[0]}x+{b[0]})}$$=$\n

$\\simplify[basic]{{c[0]}x({d[0]}x+{b[0]})+{a[0]}({d[0]}x+{b[0]})}$

\n
\n

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

\n
$=$$\\simplify[basic]{{c[0]*d[0]}x^2+{c[0]*b[0]}x+{d[0]*a[0]}x+{a[0]*b[0]}}$          (use the distributive law on each bracket)
$=$$\\simplify[basic]{{c[0]*d[0]}x^2+{d[0]*a[0]+c[0]*b[0]}x+{a[0]*b[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[basic]{({c[0]}x+{a[0]})({d[0]}x+{b[0]})}$$=$\n

$\\simplify[basic]{{c[0]*d[0]}x^2+{c[0]*b[0]}x+{d[0]*a[0]}x+{a[0]*b[0]}}$

\n
\n

          (First, Outer, Inner, Last)

\n
$=$$\\simplify[basic]{{c[0]*d[0]}x^2+{d[0]*a[0]+c[0]*b[0]}x+{a[0]*b[0]}}$          (collect like terms)
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$\\simplify[basic]{({c[1]}x+{a[1]})({d[1]}x+{b[1]})}$ = [[0]]

\n

\n

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"notallowed": {"message": "

Ensure you don't use brackets in your answer.

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Method 1 (the distributive law)

\n

We expand $\\simplify[basic]{({c[1]}x+{a[1]})({d[1]}x+{b[1]})}$ 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[basic]{({c[1]}x+{a[1]})({d[1]}x+{b[1]})}$$=$\n

$\\simplify[basic]{{c[1]}x({d[1]}x+{b[1]})+{a[1]}({d[1]}x+{b[1]})}$

\n
\n

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

\n
$=$$\\simplify[basic]{{c[1]*d[1]}x^2+{c[1]*b[1]}x+{d[1]*a[1]}x+{a[1]*b[1]}}$          (use the distributive law on each bracket)
$=$$\\simplify[basic]{{c[1]*d[1]}x^2+{d[1]*a[1]+c[1]*b[1]}x+{a[1]*b[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[basic]{({c[1]}x+{a[1]})({d[1]}x+{b[1]})}$$=$\n

$\\simplify[basic]{{c[1]*d[1]}x^2+{c[1]*b[1]}x+{d[1]*a[1]}x+{a[1]*b[1]}}$

\n
\n

          (First, Outer, Inner, Last)

\n
$=$$\\simplify[basic]{{c[1]*d[1]}x^2+{d[1]*a[1]+c[1]*b[1]}x+{a[1]*b[1]}}$          (collect like terms)
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Expand and simplify the following.

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