Simplifying before multiplying with multiple expressions | Maths

Starter quiz

Look at $4(y-7)+8(y-7)$ . Inside each bracket you can see matching __________.
- equations
- expressions ✓
- formulas
- answers
Which of the below is equivalent to $6 \times 7+2 \times 7$ ?
- $(6+2)\times 7$ ✓
- $42 \times 14$
- $(6+2) \times 14$
Expand $5(x-3)$
- $5x-3$
- $5x+3$
- $5x+15$
- $5x-15$ ✓
Which of the below are equivalent to $11 \times 6 + 11 \times 4$ ?
- $66 \times 44$
- $11 \times 10$ ✓
- $22 \times (6+4)$
- $22 \times 10$
- $11 \times (6+4)$ ✓
Expand and simplify $6(e-f)+2(f-e)$
- $8e+8f$
- $8e+4f$
- $4e+8f$
- $4e+4f$
- $4e-4f$ ✓
Match the expressions to the correct first step when expanding before simpifying.
- $5(a+3)+2(a-8)$
  
  ⇔
  
  $5a+15+2a-16$ ✓
- $5(a-3)+2(a-8)$
  
  ⇔
  
  $5a-15+2a-16$ ✓
- $5(a+3)-2(a+8)$
  
  ⇔
  
  $5a+15-2a-16$ ✓
- $5(2a+3)+2(a-8)$
  
  ⇔
  
  $10a+15+2a-16$ ✓
- $5a(a+3)+2(a-8)$
  
  ⇔
  
  $5a^2+15a+2a-16$ ✓

When you write $3(y-8)+9(y-8)$ as $12(y-8)$ you have __________ the expression.
- solved
- simplified ✓
- expanded
- factorised
Use this bar model to help you simplify the expression $5(x+6)+2(x+6)$
- $7(2x+12)$
- $7(x+6)$ ✓
- $7x+6$
- $5x+6+2x+6 \equiv 7x+12$
Which of the below cannot be simplified before it is expanded?
- $5(x+8)+7(x+8)$
- $5(y-3)+7(y-3)$
- $5(x-3)+7(y-3)$ ✓
- $5(x+8)-7(x+8)$
- $5(x+8)+7(x+8)+3(x+8)$
Match each expression with a simplified expression.
- $4(e+2)+6(e+2)$
  
  ⇔
  
  $10(e+2)$ ✓
- $4(e+2)+5(e+2)$
  
  ⇔
  
  $9(e+2)$ ✓
- $7(e+2)+3(e+2)-5(e+2)$
  
  ⇔
  
  $5(e+2)$ ✓
- $4(e+2)-5(e+2)$
  
  ⇔
  
  $-e-2$ ✓
- $4(e-2)-5(e-2)$
  
  ⇔
  
  $2-e$ ✓
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.
- Matching multipliers means you can simplify before expanding. ✓
Match each expression with a simplified expression.
- $5(y+2)+5(y+6)$
  
  ⇔
  
  $5(2y+8)$ ✓
- $5(y+2)+5(2y+6)$
  
  ⇔
  
  $5(3y+8)$ ✓
- $5(y-1)+5(y+6)$
  
  ⇔
  
  $5(2y+5)$ ✓
- $5(2y+2)-5(y+6)$
  
  ⇔
  
  $5(y-4)$ ✓
- $5(2y+2)-5(6-y)$
  
  ⇔
  
  $5(3y-4)$ ✓

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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?

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.