Expanding brackets involves removing the brackets from an expression by multiplying out the brackets. This is achieved by multiplying every term inside the bracket by the term outside the bracket.
\nExample 1- Expand:
a) Remember to multiply every term inside the brackets by the term outside:
\nWhen multiplying out double brackets, every term in the first pair of brackets must be multiplied by each term in the second. When expanding brackets, be very careful when dealing with negative numbers. Multiplying negatives has special rules: a negative times a positive gives a negative, but multiplying two negatives gives a positive:
\nExample 2- Expand : - ( a - 2)
\n- ( a- 2) = -1 * a + 1 * 2 = -a + 2
\n\n
\n
For further help, check this link - https://www.mathsisfun.com/algebra/expanding.html
\nThe expression $\\var{pmult}(\\var{pxcoeff}x+\\var{pconstant})$ is factorised (written as a product), we can expand the expression (so it is written as a sum) to get
\n[[0]] $x$ + [[1]]
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "The number in front of the bracket is multiplying the bracketed term, that is, each term in the brackets.
\n\nFor example, $3(5x+6)$ means $3\\times (5x+6)$ which means $3\\times 5x+3\\times 6$, and so expanding $3(5x+6)$ gives $15x+18$.
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{pmult*pxcoeff}", "minValue": "{pmult*pxcoeff}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{pmult*pconstant}", "minValue": "{pmult*pconstant}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": "1", "prompt": "Expand $\\var{nmult}(\\var{nxcoeff}a-\\var{-nconstant})$.
\n[[0]] $a$ + [[1]]
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "The number in front of the bracket is multiplying the bracketed term, that is, each term in the brackets. Further, recall that a negative multiplied by a negative is a positive.
\n\nFor example, $-3(5a-6)$ means $-3\\times (5a-6)$ which means $(-3)\\times 5a+(-3)\\times (-6)$, and so expanding $3(5a+6)$ gives $-15a+18$.
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{nmult*nxcoeff}", "minValue": "{nmult*nxcoeff}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{nmult*nconstant}", "minValue": "{nmult*nconstant}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": "1", "prompt": "Expand $-(\\var{cx}x-\\var{-cy}y+\\var{cc})$.
\n[[0]] $x$ + [[1]] $y$ + [[2]]
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "A negative sign in front of a bracket is a common way to signify $-1$ times the bracketed term. The result is that it changes the sign of everything in the brackets.
\n\nFor example, $-(5x-y+6)$ means $-1\\times (5x-y+6)$ which means $(-1)\\times 5x+(-1)\\times (-y)+(-1)\\times 6$, and so expanding $-(5x-y+6)$ gives $-5x+y-6$.
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{-cx}", "minValue": "{-cx}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{-cy}", "minValue": "{-cy}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{-cc}", "minValue": "{-cc}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "In the following questions, expand the bracket and express in linear variables.
\nFor more information, please check this video- https://www.youtube.com/watch?v=9r6_wDpxKjQ
", "variable_groups": [{"variables": ["pmult", "pxcoeff", "pconstant", "primes"], "name": "part a"}, {"variables": ["nmult", "nxcoeff", "nconstant"], "name": "part b"}, {"variables": ["cx", "cy", "cc"], "name": "part c"}], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"nconstant": {"definition": "random(-12..-2)", "templateType": "anything", "group": "part b", "name": "nconstant", "description": ""}, "cc": {"definition": "random(2..12)", "templateType": "anything", "group": "part c", "name": "cc", "description": ""}, "nxcoeff": {"definition": "random(2..12)", "templateType": "anything", "group": "part b", "name": "nxcoeff", "description": ""}, "pmult": {"definition": "primes[0]", "templateType": "anything", "group": "part a", "name": "pmult", "description": ""}, "pxcoeff": {"definition": "primes[1]", "templateType": "anything", "group": "part a", "name": "pxcoeff", "description": ""}, "cy": {"definition": "random(-12..1)", "templateType": "anything", "group": "part c", "name": "cy", "description": ""}, "cx": {"definition": "random(2..12)", "templateType": "anything", "group": "part c", "name": "cx", "description": ""}, "nmult": {"definition": "random(-12..-2)", "templateType": "anything", "group": "part b", "name": "nmult", "description": ""}, "primes": {"definition": "shuffle([2,3,5,7,11])[0..3]", "templateType": "anything", "group": "part a", "name": "primes", "description": ""}, "pconstant": {"definition": "primes[2]", "templateType": "anything", "group": "part a", "name": "pconstant", "description": ""}}, "metadata": {"description": "This exercise will help you in expanding brackets of linear variables
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