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      Simplifying before multiplying with multiple expressions

      I can recognise when I can simplify before multiplying expressions by their respective terms.

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      Lesson 14 of 17
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      • Year 7

      Simplifying before multiplying with multiple expressions

      I can recognise when I can simplify before multiplying expressions by their respective terms.

      Lesson details

      Key learning points

      1. Collecting together like terms simplifies the expression.
      2. Simplifying may be possible before multiplication.

      Keywords

      • Term - A term is single number or letter, or the product of numbers and/or variables. Each term is separated by the operators + and –

      • Expression - An expression contains one or more terms where each term is separated by an operator.

      Common misconception

      2(z+7)+3(z+7)+5(z+7) must be expanded first before simplifying.

      Think of 'Unitising'. What is it we are adding together? In this case, we are summing multiples of (z+7). How many lots do we have?

      Coherence is the key here. What does this resemble from their prior learning with which they are very comfortable? 3 tens + 2 tens + 4 tens makes 9 tens. 3m + 2m + 4m makes 9m.
      Teacher tip

      Licence

      This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

      Lesson video

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      Prior knowledge starter quiz

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      6 Questions

      Q1.
      Look at $$4(y-7)+8(y-7)$$. Inside each bracket you can see matching __________.

      equations
      Correct answer: expressions
      formulas
      answers

      Q2.
      Which of the below is equivalent to $$6 \times 7+2 \times 7$$?

      Correct answer: $$(6+2)\times 7$$
      $$42 \times 14$$
      $$(6+2) \times 14$$

      Q3.
      Expand $$5(x-3)$$

      $$5x-3$$
      $$5x+3$$
      $$5x+15$$
      Correct answer: $$5x-15$$

      Q4.
      Which of the below are equivalent to $$11 \times 6 + 11 \times 4$$?

      $$66 \times 44$$
      Correct answer: $$11 \times 10$$
      $$22 \times (6+4)$$
      $$22 \times 10$$
      Correct answer: $$11 \times (6+4)$$

      Q5.
      Expand and simplify $$6(e-f)+2(f-e)$$

      $$8e+8f$$
      $$8e+4f$$
      $$4e+8f$$
      $$4e+4f$$
      Correct answer: $$4e-4f$$

      Q6.
      Match the expressions to the correct first step when expanding before simpifying.

      Correct Answer:$$5(a+3)+2(a-8)$$,$$5a+15+2a-16$$
      Correct Answer:$$5(a-3)+2(a-8)$$,$$5a-15+2a-16$$
      Correct Answer:$$5(a+3)-2(a+8)$$,$$5a+15-2a-16$$
      Correct Answer:$$5(2a+3)+2(a-8)$$,$$10a+15+2a-16$$
      Correct Answer:$$5a(a+3)+2(a-8)$$,$$5a^2+15a+2a-16$$

      Assessment exit quiz

      Download quiz pdf

      6 Questions

      Q1.
      When you write $$3(y-8)+9(y-8)$$ as $$12(y-8)$$ you have __________ the expression.

      solved
      Correct answer: simplified
      expanded
      factorised

      Q2.
      Use this bar model to help you simplify the expression $$5(x+6)+2(x+6)$$

      An image in a quiz
      $$7(2x+12)$$
      Correct answer: $$7(x+6)$$
      $$7x+6$$
      $$5x+6+2x+6 \equiv 7x+12$$

      Q3.
      Which of the below cannot be simplified before it is expanded?

      $$5(x+8)+7(x+8)$$
      $$5(y-3)+7(y-3)$$
      Correct answer: $$5(x-3)+7(y-3)$$
      $$5(x+8)-7(x+8)$$
      $$5(x+8)+7(x+8)+3(x+8)$$

      Q4.
      Match each expression with a simplified expression.

      Correct Answer:$$4(e+2)+6(e+2)$$,$$10(e+2)$$
      Correct Answer:$$4(e+2)+5(e+2)$$,$$9(e+2)$$
      Correct Answer:$$7(e+2)+3(e+2)-5(e+2)$$,$$5(e+2)$$
      Correct Answer:$$4(e+2)-5(e+2)$$,$$-e-2$$
      Correct Answer:$$4(e-2)-5(e-2)$$,$$2-e$$

      Q5.
      Which of the below is true for $$8y(x-4)+8y(x-5)$$?

      $$x-4$$ and $$x-5$$ are not matching expressions so you can not simplify.
      You have to expand first before simplifying.
      Correct answer: Matching multipliers means you can simplify before expanding.

      Q6.
      Match each expression with a simplified expression.

      Correct Answer:$$5(y+2)+5(y+6)$$,$$5(2y+8)$$
      Correct Answer:$$5(y+2)+5(2y+6)$$,$$5(3y+8)$$
      Correct Answer:$$5(y-1)+5(y+6)$$,$$5(2y+5)$$
      Correct Answer:$$5(2y+2)-5(y+6)$$,$$5(y-4)$$
      Correct Answer:$$5(2y+2)-5(6-y)$$,$$5(3y-4)$$

      Lesson appears in

      UnitMaths / Expressions and equations

      Maths

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