We now learn how to factor quadratics using the difference of two squares formula.
In particular we can factor quadratics looking like: \[ax^2-k^2 = 0\] Notice: comparing this to the generic quadratic \(ax^2 + bx +c\) we can see that there is no \(x\) term, in other words \(b = 0\).
Remember, the difference of two squares formula was: \[a^2-b^2 =\begin{pmatrix}a+b\end{pmatrix}.\begin{pmatrix}a-b\end{pmatrix} \] This formula can be used to show, for instance, that: \[x^2-25 = \begin{pmatrix}x-5\end{pmatrix}.\begin{pmatrix}x+5\end{pmatrix}\] or that: \[4x^2 - 9 = \begin{pmatrix}2x-3\end{pmatrix}.\begin{pmatrix}2x+3\end{pmatrix}\] We learn the method in the tutorial below.
In the following tutorial we learn how to use the difference of two squares to factorize quadratics.
Write each of the following quadratics in factored form:
The method for factoring quadratics using the difference of two squares can be used to solve quadratic equations that can be written: \[ax^2 - k^2 = 0\] This is illustrated in the following tutorial.
Use factorization to solve each of the following quadratic equations:
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