Cards In This Deck

• $$\begin{gathered} \text{True or False?} \\ (x+3{)}^2=x^2+9 \end{gathered}$$
  $$\begin{gathered} \text{False} \\ \text{Correct Answer: }{x}^2+6x+9 \end{gathered}$$
• $$\begin{gathered} \text{True or False?} \\ -2x(3x-5)=-6x^2-10x \end{gathered}$$
  $$\begin{gathered} \text{❌ False} \\ \text{✅ Correct Answer: }-6x^2+10x \end{gathered}$$
• $$\begin{gathered} \text{What is the safest first step to expand three linear terms?} \\ \text{e.g., }(x+1)(x+2)(x+3) \end{gathered}$$
  $\text{Expand two brackets first to get a quadratic, then multiply the result by the third bracket.}$
• $$\begin{gathered} \text{True or False?} \\ \text{When expanding }-3x(7x-4)\text{, the result is }-21x^2-12x\text{.} \end{gathered}$$
  $$\begin{gathered} \text{False} \\ \text{Correct Answer: }-21x^2+12x \end{gathered}$$
• $\text{When factorising a complicated expression like }3x^3-12x\text{, what should you look for first?}$
  $\text{Look for a common factor to take out.}$
• $$\begin{gathered} \text{True or False?} \\ {x}^2+16\text{ factorises to }(x+4)(x+4) \end{gathered}$$
  $$\begin{gathered} \text{❌ False} \\ \text{✅ Correct Answer: It does not factorise (over real numbers).} \end{gathered}$$
• $$\begin{gathered} \text{True or False?} \\ {x}^2+9\text{ factorises to }(x+3)(x+3)\text{.} \end{gathered}$$
  $$\begin{gathered} \text{False} \\ \text{Correct Answer: It does not factorise.} \end{gathered}$$
• $\text{When factorising }{x}^4-y^4\text{, which method should you recognize immediately?}$
  $\text{Difference of Two Squares (DOTS).}$
• $$\begin{gathered} \text{What is the first thing you should check for when asked to factorise an expression completely? } \\ \text{e.g., }3x^2+9x \end{gathered}$$
  $\text{Check for a common factor.}$
• $$\begin{gathered} \text{True or False?} \\ \text{To integrate }\int (3x-1{)}^2 \\ ,dx\text{, you should use the reverse chain rule to get }\frac{(3x-1{)}^3}{3}+c\text{?} \end{gathered}$$
  $$\begin{gathered} \text{❌ **False** (It leads to the wrong coefficient)} \\ \text{✅ **P1 Method:**} \\ \text{**Expand** the brackets first: }\int (9x^2-6x+1) \\ ,dx \\ \text{Then integrate term by term: }3x^3-3x^2+x+c \end{gathered}$$