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This question is made up of 10 exercises to practice the multiplication of brackets by a single term.

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Expand the expressions below by multiplying each of the terms inside the brackets by the term outside. Give each answer in its simplest form.

Expand brackets using the general formula $\\displaystyle a(x+c)=ax+ac$. This means we multiply each term inside the brackets by the term outside the brackets.

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It is easy to forget that the sign outside the brackets also needs to be involved in the multiplication so remember that when two of the same sign are multiplied, the resultant term is positive and when opposite signs are multiplied, the result is negative.

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#### a)

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\\\begin{align} \\simplify[terms]{{a[1]}({a[2]}x+{a[3]})}&= \\simplify[!collectNumbers]{({a[1]}{a[2]})x+({a[1]}{a[3]})}\\\\& =\\simplify{{a[1]}*{a[2]}x+{a[1]}{a[3]}}\\text{.} \\end{align} \

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#### b)

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\\\begin{align} \\simplify[terms]{{a[4]}({a[5]}x+{a[6]})}&= \\simplify[!collectNumbers]{{a[4]}{a[5]}x+{a[4]}{a[6]}}\\\\&= \\simplify{{a[4]}*{a[5]}x+{a[4]}{a[6]}}\\text{.} \\end{align} \

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#### c)

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\\\begin{align} \\simplify[terms]{{a[7]}({a[8]}x^2+{a[9]}y)}&= \\simplify[!collectNumbers]{{a[7]}{a[8]}x^2+{a[7]}{a[9]}y}\\\\&= \\simplify{{a[7]}*{a[8]}x^2+{a[7]}*{a[9]}y}\\text{.} \\end{align} \

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#### d)

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\\\begin{align} \\simplify[terms]{{a[10]}({a[11]}x^2+{a[12]}y)}&= \\simplify[!collectNumbers]{{a[10]}{a[11]}x^2+{a[10]}{a[12]}y}\\\\&= \\simplify{{a[10]}*{a[11]}x^2+{a[10]}*{a[12]}y}\\text{.} \\end{align} \

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#### e)

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\\\begin{align} \\simplify[terms]{{a[13]}x({a[14]}x^2+{a[15]}x+{a[16]})}&= \\simplify[!collectNumbers]{{a[13]}x{a[14]}x^2+{a[13]}x{a[15]}x+{a[13]}x{a[16]}}\\\\&= \\simplify{{a[13]}{a[14]}x^3+{a[13]}{a[15]}x^2+{a[13]}{a[16]}x}\\text{.} \\end{align} \

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#### f)

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\\\begin{align} \\simplify[terms]{{a[17]}x({a[18]}x^2+{a[19]}x+{a[20]})}&= \\simplify[!collectNumbers]{{a[17]}x{a[18]}x^2+{a[17]}x{a[19]}x+{a[17]}x{a[20]}}\\\\&= \\simplify{{a[17]}{a[18]}x^3+{a[17]}{a[19]}x^2+{a[17]}{a[20]}x}\\text{.} \\end{align} \

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#### g)

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\\\begin{align} \\simplify[terms]{{a[21]}x({a[22]}x^2+{a[23]}x)+{a[24]}x^2+{a[25]}x^3}&= \\simplify[!collectNumbers]{x^2({a[21]}{a[23]})+x^2{a[24]}+x^3({a[21]}{a[22]})+x^3{a[25]}}\\\\&= \\simplify[!collectNumbers]{x^2({a[21]}{a[23]}+{a[24]})+x^3({a[21]}{a[22]}+{a[25]})}\\\\&= \\simplify{x^2({a[21]}{a[23]}+{a[24]})+x^3({a[21]}{a[22]}+{a[25]})}\\text{.} \\end{align} \

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#### h)

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\\\begin{align} \\simplify[terms]{({a[26]}x^2+{a[27]}x^3)+{a[28]}x({a[29]}x^2+{a[30]}x)}&= \\simplify[!collectNumbers]{x^2({a[26]})+x^2({a[28]}{a[30]})+x^3({a[28]}{a[29]})+x^3({a[27]})}\\\\&= \\simplify[!collectNumbers]{x^2({a[26]}+{a[28]}{a[30]})+x^3({a[28]}{a[29]}+{a[27]})}\\\\&= \\simplify{x^2({a[26]}+{a[28]}{a[30]})+x^3({a[28]}{a[29]}+{a[27]})}\\text{.} \\end{align} \

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#### i)

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\\\begin{align} \\simplify[terms]{{a[31]}({a[32]}x+{a[33]}y)+{a[34]}x({a[42]}+{a[35]}y)}&= \\simplify[!collectNumbers]{({a[31]}{a[32]})x+({a[34]}{a[42]})x+{a[31]}{a[33]}y+{a[34]}{a[35]}x*y}\\\\&= \\simplify[!collectNumbers]{({a[31]}{a[32]}+{a[34]}{a[42]})x+{a[31]}{a[33]}y+{a[34]}{a[35]}x*y}\\\\&= \\simplify{({a[31]}{a[32]}+{a[34]}{a[42]})x+{a[31]}{a[33]}y+{a[34]}{a[35]}x*y}\\text{.} \\end{align} \

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#### j)

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\\\begin{align} \\simplify[terms]{{a[36]}a^2({a[37]}+{a[38]}b)+{a[39]}b^2({a[40]}a+{a[41]}b)}&= \\simplify[!collectNumbers]{{a[37]}{a[36]}a^2+{a[38]}{a[36]}a^2b+{a[40]}{a[39]}a*b^2+{a[39]}{a[41]}b^3}\\\\&= \\simplify{{a[37]}{a[36]}a^2+{a[38]}{a[36]}a^2b+{a[40]}{a[39]}a*b^2+{a[39]}{a[41]}b^3}\\text{.} \\end{align} \

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$\\simplify{{a[1]}({a[2]}x+{a[3]})}=$ [[0]]

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It doesn't look like you've expanded - make sure you don't use any brackets in your answer.

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$\\simplify{{a[4]}({a[5]}x+{a[6]})}=$ [[0]]

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It doesn't look like you've expanded - make sure you don't use any brackets in your answer.

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$\\simplify{{a[7]}({a[8]}x^2+{a[9]}y)}=$ [[0]]

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It doesn't look like you've expanded - make sure you don't use any brackets in your answer.

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$\\simplify{{a[10]}({a[11]}x^2+{a[12]}y)}=$ [[0]]

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It doesn't look like you've expanded - make sure you don't use any brackets in your answer.

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$\\simplify{{a[13]}x({a[14]}x^2+{a[15]}x+{a[16]})}=$ [[0]]

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It doesn't look like you've expanded - make sure you don't use any brackets in your answer.

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$\\simplify{{a[21]}x({a[22]}x^2+{a[23]}x)+{a[24]}x^2+{a[25]}x^3}=$ [[0]]

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$\\simplify{({a[26]}x^2+{a[27]}x^3)+{a[28]}x({a[29]}x^2+{a[30]}x)}=$ [[0]]

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$\\simplify{{a[31]}({a[32]}x+{a[33]}y)+{a[34]}x({a[42]}+{a[35]}y)}=$ [[0]]

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It doesn't look like you've expanded - make sure you don't use any brackets in your answer.

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