Multiplying Algebraic Expressions

Example:

Evaluate:

a) 2p(3pq – 5qr)

b)

Solution:

a) 2p(3pq – 5qr)

= [2p× 3pq] + [2p× (–5qr)]

= 6p²q – 10pqr

Next, we will also consider the multiplication of two algebraic expressions:

(a + b)(c + d)

Such an operation is called ‘expanding the expression ’. To expand the expression, we multiply each term in the first pair of brackets by every term in the second pair of brackets.

Example:

Expand the following:

a) (y – 3)(2y + 5)

b) (a + b)²

Solution:

a) (y – 3)(2y + 5)

= y(2y+ 5) – 3(2y + 5)

= (y × 2y) + (y × 5) + (–3 × 2y) + (–3 × 5)

= 2y² + 5y – 6y – 15

= 2y² – y – 15

b) (a + b)²

= (a + b)(a + b) = a(a + b) + b(a + b)

= a² + ab + ab + b²

= a² + 2ab + b²

Here are some common expansions that you will find useful to remember:

(a + b)² = a² + 2ab + b²

(a – b)² = a² – 2ab + b²

(a + b)(a – b) = a² – b²

The following video shows more examples of multiplying expressions.

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