// Numbas version: finer_feedback_settings {"name": "Heidi's copy of 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": [{"question_groups": [{"questions": [], "pickingStrategy": "all-ordered", "pickQuestions": 0, "name": ""}], "showQuestionGroupNames": false, "variables": {"a": {"group": "Ungrouped variables", "definition": "shuffle(-12..12 except 0)[0..4]", "templateType": "anything", "name": "a", "description": ""}, "b": {"group": "Ungrouped variables", "definition": "shuffle(-12..12 except 0)[0..4]", "templateType": "anything", "name": "b", "description": ""}}, "metadata": {"description": "", "notes": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "name": "Heidi's copy of Expanding a binomial product (monic factors)", "advice": "", "functions": {}, "preamble": {"js": "", "css": ""}, "ungrouped_variables": ["a", "b"], "parts": [{"gaps": [{"variableReplacements": [], "checkvariablenames": true, "notallowed": {"showStrings": false, "partialCredit": 0, "message": "

Ensure you don't use brackets in your answer.

", "strings": ["(", ")"]}, "marks": 1, "vsetrangepoints": 5, "expectedvariablenames": ["x"], "showCorrectAnswer": true, "showpreview": true, "checkingaccuracy": 0.001, "answer": "x^2+{a[0]+b[0]}x+{a[0]*b[0]}", "checkingtype": "absdiff", "variableReplacementStrategy": "originalfirst", "vsetrange": [0, 1], "type": "jme", "scripts": {}}], "stepsPenalty": "1", "variableReplacements": [], "prompt": "

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

", "variableReplacementStrategy": "originalfirst", "steps": [{"variableReplacements": [], "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)

", "variableReplacementStrategy": "originalfirst", "marks": 0, "scripts": {}, "type": "information", "showCorrectAnswer": true}], "marks": 0, "scripts": {}, "type": "gapfill", "showCorrectAnswer": true}, {"gaps": [{"variableReplacements": [], "checkvariablenames": true, "notallowed": {"showStrings": false, "partialCredit": 0, "message": "

Ensure you don't use brackets in your answer.

", "strings": ["(", ")"]}, "marks": 1, "vsetrangepoints": 5, "expectedvariablenames": ["x"], "showCorrectAnswer": true, "showpreview": true, "checkingaccuracy": 0.001, "answer": "x^2+{a[1]+b[1]}x+{a[1]*b[1]}", "checkingtype": "absdiff", "variableReplacementStrategy": "originalfirst", "vsetrange": [0, 1], "type": "jme", "scripts": {}}], "stepsPenalty": "1", "variableReplacements": [], "prompt": "

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

", "variableReplacementStrategy": "originalfirst", "steps": [{"variableReplacements": [], "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.

", "strings": ["(", ")"]}, "marks": 1, "vsetrangepoints": 5, "expectedvariablenames": ["m"], "showCorrectAnswer": true, "showpreview": true, "checkingaccuracy": 0.001, "answer": "m^2+{a[2]+b[2]}m+{a[2]*b[2]}", "checkingtype": "absdiff", "variableReplacementStrategy": "originalfirst", "vsetrange": [0, 1], "type": "jme", "scripts": {}}], "stepsPenalty": "1", "variableReplacements": [], "prompt": "

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

", "variableReplacementStrategy": "originalfirst", "steps": [{"variableReplacements": [], "prompt": "

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)

Ensure you don't use brackets in your answer.

", "strings": ["(", ")"]}, "marks": 1, "vsetrangepoints": 5, "expectedvariablenames": ["t"], "showCorrectAnswer": true, "showpreview": true, "checkingaccuracy": 0.001, "answer": "t^2+{a[3]+b[3]}t+{a[3]*b[3]}", "checkingtype": "absdiff", "variableReplacementStrategy": "originalfirst", "vsetrange": [0, 1], "type": "jme", "scripts": {}}], "stepsPenalty": "1", "variableReplacements": [], "prompt": "

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

", "variableReplacementStrategy": "originalfirst", "steps": [{"variableReplacements": [], "prompt": "

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)

", "variableReplacementStrategy": "originalfirst", "marks": 0, "scripts": {}, "type": "information", "showCorrectAnswer": true}], "marks": 0, "scripts": {}, "type": "gapfill", "showCorrectAnswer": true}], "rulesets": {}, "variablesTest": {"condition": "", "maxRuns": "127"}, "variable_groups": [], "tags": ["binomial", "binomial product", "distributive law", "expanding", "factorisation", "Factorisation", "factors", "Factors", "monic", "quadratic"], "statement": "

Expand and simplify the following.

", "type": "question", "contributors": [{"name": "Heidi Steele", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1773/"}]}]}], "contributors": [{"name": "Heidi Steele", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1773/"}]}