Question

special case | example
(a + b)(a - b) = a² - b² | (x + 2)(x - 2) =
(a + b)² = (a + b)(a + b) = a² + 2ab + b² | (x + 3)² =
(a - b)² = (a - b)(a - b) = a² - 2ab + b² | (x - 3)² =

Explanation:

For \((x + 2)(x - 2)\):

Step1: Identify the formula

We use the difference of squares formula \((a + b)(a - b)=a^{2}-b^{2}\), here \(a = x\) and \(b = 2\).

Step2: Apply the formula

Substitute \(a=x\) and \(b = 2\) into the formula, we get \((x+2)(x - 2)=x^{2}-2^{2}=x^{2}-4\).

For \((x + 3)^{2}\):

Step1: Identify the formula

We use the perfect square formula \((a + b)^{2}=a^{2}+2ab + b^{2}\), here \(a=x\) and \(b = 3\).

Step2: Apply the formula

Substitute \(a = x\) and \(b=3\) into the formula, we have \(a^{2}=x^{2}\), \(2ab=2\times x\times3 = 6x\), \(b^{2}=3^{2}=9\). So \((x + 3)^{2}=x^{2}+6x + 9\).

For \((x - 3)^{2}\):

Step1: Identify the formula

We use the perfect square formula \((a - b)^{2}=a^{2}-2ab + b^{2}\), here \(a=x\) and \(b = 3\).

Step2: Apply the formula

Substitute \(a = x\) and \(b = 3\) into the formula, we get \(a^{2}=x^{2}\), \(2ab=2\times x\times3=6x\), \(b^{2}=3^{2} = 9\). So \((x-3)^{2}=x^{2}-6x + 9\).

Answer:

s:
\((x + 2)(x - 2)=\boldsymbol{x^{2}-4}\)

\((x + 3)^{2}=\boldsymbol{x^{2}+6x + 9}\)

\((x - 3)^{2}=\boldsymbol{x^{2}-6x + 9}\)