## Sum and Difference of Two cubes

In 2013 alevel, factorisation of the difference of two cubes can be used in one of the questions

Here are the formulas students should remember:

Students can use the mnemonic “SOAP” to help them remember the formula.

S: Same sign

O: Opposite sign

A: Always

P: Positive

## Juggling: shortcut to long division

Juggling is a shortcut to long division, especially in the case where the degree of the numerator is the same as the denominator. In H2 math, juggling is a useful technique in finding the asymptote of graphs and integration.

## Trigo “Product to Sum” formula

Trigo “Sum to Product” formula is given in the math formula list MF26. However,  “Product to Sum” formula is not in the formula list. Yet, students are often required to use the “Product to Sum” formula in mathematical induction or integration. Hence, knowing how to derive the “Product to Sum” formula from “Sum to Product” formula is critical.

“Sum to Product” formula

To derive the “Product to Sum” formula

Let P = X+Y and Q= X-Y

Substitute into the “Sum to Product” formula, we derived the “Product to Sum” formula

## Try this long division problem!

Many students, including JC H2 math students, have difficulty doing long division when it comes to complex problems.

Try this problem to test or sharpen your long division skills.

Question

If  is a factor of , prove by long division that

Solution

## Partial fraction: Cover-up rule

Partial fraction is commonly used in binomial expansion, method of difference and integration.

When the divisor consists only of linear factors, cover up rule can be used to find the constants in the partial fraction quickly.

Example

Express  in partial fraction.

By cover up rule,

Therefore

0 = A+C

Therefore,