// Numbas version: finer_feedback_settings {"name": "Expanding a binomial product (monic factors)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"rulesets": {}, "variable_groups": [], "tags": [], "parts": [{"variableReplacementStrategy": "originalfirst", "steps": [{"variableReplacementStrategy": "originalfirst", "customName": "", "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "scripts": {}, "marks": 0, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "useCustomName": false, "unitTests": [], "type": "information", "prompt": "

Method 1 (the distributive law)

We expand $\\simplify{(x+{a[0]})(x+{b[0]})}$ 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

$\\simplify{(x+{a[0]})(x+{b[0]})}$	$=$	\n $\\simplify{x(x+{b[0]})+{a[0]}(x+{b[0]})}$ \n	\n (each term in one bracket times the entire other bracket) \n
	$=$	$\\simplify{x^2+{b[0]}x+{a[0]}x+{a[0]*b[0]}}$	(use the distributive law on each bracket)
	$=$	$\\simplify{x^2+{b[0]+a[0]}x+{a[0]*b[0]}}$	(collect like terms)

Method 2 (FOIL)

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

$\\simplify{(x+{a[0]})(x+{b[0]})}$	$=$	\n $\\simplify[basic]{x^2+{b[0]}x+{a[0]}x+{a[0]*b[0]}}$ \n	\n (First, Outer, Inner, Last) \n
	$=$	$\\simplify{x^2+{b[0]+a[0]}x+{a[0]*b[0]}}$	(collect like terms)

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Ensure you don't use brackets in your answer.

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

"}, {"variableReplacementStrategy": "originalfirst", "steps": [{"variableReplacementStrategy": "originalfirst", "customName": "", "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "scripts": {}, "marks": 0, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "useCustomName": false, "unitTests": [], "type": "information", "prompt": "

Method 1 (the distributive law)

We expand $\\simplify{(x+{a[1]})(x+{b[1]})}$ 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

$\\simplify{(x+{a[1]})(x+{b[1]})}$	$=$	\n $\\simplify{x(x+{b[1]})+{a[1]}(x+{b[1]})}$ \n	\n (each term in one bracket times the entire other bracket) \n
	$=$	$\\simplify{x^2+{b[1]}x+{a[1]}x+{a[1]*b[1]}}$	(use the distributive law on each bracket)
	$=$	$\\simplify{x^2+{b[1]+a[1]}x+{a[1]*b[1]}}$	(collect like terms)

Method 2 (FOIL)

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

$\\simplify{(x+{a[1]})(x+{b[1]})}$	$=$	\n $\\simplify[basic]{x^2+{b[1]}x+{a[1]}x+{a[1]*b[1]}}$ \n	\n (First, Outer, Inner, Last) \n
	$=$	$\\simplify{x^2+{b[1]+a[1]}x+{a[1]*b[1]}}$	(collect like terms)

Ensure you don't use brackets in your answer.

"}, "checkingAccuracy": 0.001, "customMarkingAlgorithm": "", "answer": "x^2+{a[1]+b[1]}x+{a[1]*b[1]}"}], "unitTests": [], "type": "gapfill", "prompt": "

$\\simplify{(x+{a[1]})(x+{b[1]})}$ = [[0]]

Method 1 (the distributive law)

We expand $\\simplify{(m+{a[2]})(m+{b[2]})}$ 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

$\\simplify{(m+{a[2]})(m+{b[2]})}$	$=$	\n $\\simplify{m(m+{b[2]})+{a[2]}(m+{b[2]})}$ \n	\n (each term in one bracket times the entire other bracket) \n
	$=$	$\\simplify{m^2+{b[2]}m+{a[2]}m+{a[2]*b[2]}}$	(use the distributive law on each bracket)
	$=$	$\\simplify{m^2+{b[2]+a[2]}m+{a[2]*b[2]}}$	(collect like terms)

Method 2 (FOIL)

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

$\\simplify{(m+{a[2]})(m+{b[2]})}$	$=$	\n $\\simplify[basic]{m^2+{b[2]}m+{a[2]}m+{a[2]*b[2]}}$ \n	\n (First, Outer, Inner, Last) \n
	$=$	$\\simplify{m^2+{b[2]+a[2]}m+{a[2]*b[2]}}$	(collect like terms)

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Ensure you don't use brackets in your answer.

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$\\simplify{(m+{a[2]})(m+{b[2]})}$ = [[0]]

Method 1 (the distributive law)

We expand $\\simplify{(t+{a[3]})(t+{b[3]})}$ 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

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

$=$

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

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

$=$

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

(use the distributive law on each bracket)

$=$

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

(collect like terms)

Method 2 (FOIL)

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

$\\simplify{(t+{a[3]})(t+{b[3]})}$	$=$	\n $\\simplify[basic]{t^2+{b[3]}t+{a[3]}t+{a[3]*b[3]}}$ \n	\n (First, Outer, Inner, Last) \n
	$=$	$\\simplify{t^2+{b[3]+a[3]}t+{a[3]*b[3]}}$	(collect like terms)

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Ensure you don't use brackets in your answer.

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

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Expand and simplify the following.

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