Multiplying and simplifying with multiple expressions | Maths

Starter quiz

Without changing its value, we could write the expression $5x+7+3x+8$ more efficiently by ______ it.
- 'simplifying' ✓
Expand $8(x+3)$
- $8+x+3$
- $8x+24$ ✓
- $8x+3$
- $x+24$
Match the expressions to the simplified expressions.
- $3x + 7 + 4x + 6$
  
  ⇔
  
  $7x +13$ ✓
- $7x + 3 + 6x + 4$
  
  ⇔
  
  $13x + 7$ ✓
- $7x + 13 + 3x -3$
  
  ⇔
  
  $10x+10$ ✓
- $6x -7 -13x -3$
  
  ⇔
  
  $-7x-10$ ✓
- $3x + 13 + 4x -3$
  
  ⇔
  
  $7x+10$ ✓
Match the expressions.
- $7(y+3)$
  
  ⇔
  
  $7y+21$ ✓
- $-7(y-3)$
  
  ⇔
  
  $21-7y$ ✓
- $-7(y+3)$
  
  ⇔
  
  $-7y-21$ ✓
- $7(y-3)$
  
  ⇔
  
  $7y-21$ ✓
Simplify $10x+3-7x-10$
- $3x+7$
- $-3x+7$
- $3x-7$ ✓
- $-3x-7$
Expand $-f(3e+2f-g)$
- $-3e^2f-2f^2+fg$
- $-3ef-f^2+fg$
- $-3ef-2f^2-fg$
- $-3ef-2f^2+fg$ ✓

In algebra, when we write the expression $6(y-7)$ as $6y-42$ it is called __________.
- factorising
- expanding ✓
- simplifying ✓
- dividing
Expand $-2x(5-x)$
- $-10x+2x^2$ ✓
- $3x-x$
- $-10x-2x^2$
- $10x+2x^2$
Expand and simplify $2(y+3)+7(y-1)$
- $2y+6-7y-7 \equiv -y-1$
- $2y+6+7y-7 \equiv 9y-1$ ✓
- $2y+6+7y-7 \equiv 9y+1$
- $2y+3+7y-1 \equiv 9y+2$
Match the expressions.
- $5(x+4)+3(x+8)$
  
  ⇔
  
  $8x+44$ ✓
- $5(x+4)+8(x+3)$
  
  ⇔
  
  $13x+44$ ✓
- $4(x+5)+3(x+8)$
  
  ⇔
  
  $7x+44$ ✓
- $4(x+5)+8(x-3)$
  
  ⇔
  
  $12x-4$ ✓
- $4(x-5)+8(x+3)$
  
  ⇔
  
  $12x+4$ ✓
Expand and simplify $2d(d-3)-5(d+e)$
- $2d^2+11d-5e$
- $2d^2-8d-5e$
- $2d^2-11d+5e$
- $2d^2-11d-5e$ ✓
Match the expressions.
- $x(x+y-7)-3x(x-2y)$
  
  ⇔
  
  $-2x^2-7x+7xy$ ✓
- $x(x+y-7)+3x(x-2y)$
  
  ⇔
  
  $4x^2-7x-5xy$ ✓
- $-x(x+y-7)+3x(x-2y)$
  
  ⇔
  
  $2x^2+7x-7xy$ ✓
- $-x(x+y-7)-3x(x-2y)$
  
  ⇔
  
  $-4x^2+7x+5xy$ ✓

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Pupils may think 5(y+1)-2(y+3) = 5y+5-2y+6

Correct use of the distributive law with either algebra tiles or an area model will demonstrate why this is wrong.

Simplify - To simplify an expression is to write it in a more efficient and compact form without affecting the value of the original expression.
Like terms - Like terms are terms that have the same set of variables and corresponding exponents.