Expanding and simplifying questions with answers

Questions

1. Question 1One bracket

   Expand and simplify $3(5x + 4)$.

   Show the worked solution

   1. Step 1: Multiply each term in the bracket by the number outside$3(5x + 4) = 15x + 12$
2. Question 2Adding two brackets

   Expand and simplify $4(3x - 9) + 6(x + 4)$.

   Show the worked solution

   1. Step 1: Multiply every term in each bracket by the term in front of it (a minus in front changes both signs)$4(3x - 9) + 6(x + 4) = 12x - 36 + 6x + 24$
   2. Step 2: Collect like terms$= 18x - 12$
3. Question 3Subtracting a bracket

   Expand and simplify $4(4x - 8) - 4(x - 5)$.

   Show the worked solution

   1. Step 1: Multiply every term in each bracket by the term in front of it (a minus in front changes both signs)$4(4x - 8) - 4(x - 5) = 16x - 32 - 4x + 20$
   2. Step 2: Collect like terms$= 12x - 12$
4. Question 4Two letters

   Expand and simplify $2(5x + 5y) - 5(5x - 4y)$.

   Show the worked solution

   1. Step 1: Multiply every term in each bracket by the term in front of it (a minus in front changes both signs)$2(5x + 5y) - 5(5x - 4y) = 10x + 10y - 25x + 20y$
   2. Step 2: Collect like terms$= -15x + 30y$
5. Question 5x outside a bracket

   Expand and simplify $-x(4x + 6) + 5(x + 7)$.

   Show the worked solution

   1. Step 1: Multiply every term in each bracket by the term in front of it (a minus in front changes both signs)$-x(4x + 6) + 5(x + 7) = -4x^{2} - 6x + 5x + 35$
   2. Step 2: Collect like terms$= -4x^{2} - x + 35$
6. Question 6The operation in words: subtract the sum of A and B from C

   $A = 3x^{2} + 8 - x$, $B = 5x - 3 + 3x^{2}$ and $C = -6x - 4 + 4x^{2}$. Subtract the sum of $A$ and $B$ from $C$. Give your answer in its simplest form.

   Show the worked solution

   1. Step 1: Write the words with A, B and C (“subtract X from Y” means Y − X)$C - (A + B)$
   2. Step 2: Put each expression in for its letter, in brackets$(-6x - 4 + 4x^{2}) - [(3x^{2} + 8 - x) + (5x - 3 + 3x^{2})]$
   3. Step 3: Remove the brackets: a minus in front of a bracket changes the sign of every term inside$= -6x - 4 + 4x^{2} - 3x^{2} - 8 + x - 5x + 3 - 3x^{2}$
   4. Step 4: Collect like terms$= -2x^{2} - 10x - 9$