Loading...

Difference of two squares (DOTS)
\[ a^2 - b^2 = (a + b)(a - b) \]
The expressions \(a + b\) and \(a - b\) are called conjugates.

Conjugates are formed by changing the sign between two terms.

More examples:

ExpressionConjugate
\(x+y\)\(x-y\)
\(x+3\)\(x-3\)
\(x+\sqrt{5}\)\(x-\sqrt{5}\)

Factorise the following expressions:

Exercise #1

\[ \,\,\, 1) \quad x^2 - 121 \] \[ \,\,\, 2) \quad x^2 - 121 \] \[ \,\,\, 3) \quad x^2 - 9 \] \[ \,\,\, 4) \quad x^2 - 144 \] \[ \,\,\, 5) \quad x^2 - 144 \]

\[ \,\,\, 1) \quad x^2 - 121 = (x + 11)(x - 11) \] \[ \,\,\, 2) \quad x^2 - 121 = (x + 11)(x - 11) \] \[ \,\,\, 3) \quad x^2 - 9 = (x + 3)(x - 3) \] \[ \,\,\, 4) \quad x^2 - 144 = (x + 12)(x - 12) \] \[ \,\,\, 5) \quad x^2 - 144 = (x + 12)(x - 12) \]

Exercise #2

\[ \,\,\, 1) \quad x^2 - 53 \] \[ \,\,\, 2) \quad x^2 - 24 \] \[ \,\,\, 3) \quad x^2 - 22 \] \[ \,\,\, 4) \quad x^2 - 31 \] \[ \,\,\, 5) \quad x^2 - 73 \]

\[ \,\,\, 1) \quad x^2 - 53 = (x + \sqrt{53})(x - \sqrt{53}) \] \[ \,\,\, 2) \quad x^2 - 24 = (x + \sqrt{24})(x - \sqrt{24}) \] \[ \,\,\, 3) \quad x^2 - 22 = (x + \sqrt{22})(x - \sqrt{22}) \] \[ \,\,\, 4) \quad x^2 - 31 = (x + \sqrt{31})(x - \sqrt{31}) \] \[ \,\,\, 5) \quad x^2 - 73 = (x + \sqrt{73})(x - \sqrt{73}) \]

Quadratics