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Year 10 Interactive Maths - Second Edition


Binomials

A binomial expression is an expression consisting of two terms.

Examples of binomial expressions


Product of Binomial Expressions

The product of two binomial expressions is called a binomial product. 

For example, (x + 2)(x + 8) is a binomial product.

The expansion (x + 2)(x + 8) can be considered as representative of the area of a rectangle of length (x + 8) units and width (x + 2) units.

The binomial product (x + 2)(x + 8) is illustrated in terms of the area of a rectangle.

This can be split up into two parts as follows:

The binomial product (x + 2)(x + 8) is illustrated in terms of two rectangular areas.

Expanding the binomial product using the area of two rectangles.

Algebraic Method

The algebraic method of expanding a binomial product using the Distributive Law.

Setting out:

Often, we set out the solution as follows:

The usual way of setting out the solution to expanding a binomial product using the Distributive Law.


Example 5

Example 5 involves expanding and simplifying binomial products.

Solution:

Use the Distributive Law to expand the binomial product, then collect like terms and write the solution with descending powers of x.

Use the Distributive Law to expand the binomial product, then collect like terms and write the solution with descending powers of p.

Use the Distributive Law to expand the binomial product, then collect like terms and write the solution with descending powers of a.


Key Terms

binomial expression, binomial product


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