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WAEC Mathematics 2012 Paper

Question : 9

Total: 49

Simplify:

\frac{54k^2 - 6}{3k + 1}

Solution:

Concept:

Factorization and cancellation of a common algebraic factor.

Explanation:

Factor the numerator as a difference of squares.

\frac{54k^2 - 6}{3k + 1} = \frac{6(9k^2 - 1)}{3k + 1}

Now

9k^2 - 1 = (3k)^2 - 1^2 = (3k - 1)(3k + 1)

So the expression becomes

\frac{6(3k - 1)(3k + 1)}{3k + 1}

Cancel the common factor

(3k + 1)

The simplified form is

6(3k - 1)

Answer:

6(3k - 1)

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