Algebra

Quadratic Difference Factorization

 

Quadratic Difference Factorization
\(a^2 - b^2 = (a + b)(a - b)\)

Example 01

Factorize \(9b^2 - 400\)

\begin{equation*} \begin{split} & (3b)^2 - 20^2 \\\\ & (3b + 20)(3b - 20) \end{split} \end{equation*}

Example 02

Factorize \(\dfrac{16}{25} - 4p^2\)

\begin{equation*} \begin{split} & \left(\frac {4}{5}\right)^2 - (2p)^2\\\\ & \left(\frac{4}{5} + 2p \right) \left(\frac{4}{5} - 2p \right) \end{split} \end{equation*}

 

Example 03

Expand \((4x + 5)(4x - 5)\)

\begin{equation*} \begin{split} & (4x)^2 - 5^2\\\\ & 16x^2 - 25 \end{split} \end{equation*}

Example 04

Expand \((7m^2 - 6n^3)(7m^2 + 6n^3)\)

\begin{equation*} \begin{split} & (7m^2)^2 - (6n^3)^2\\\\ & 49m^4 - 36n^6 \end{split} \end{equation*}

 

Exercise

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