Multiplying terms and expressions

Algebraic terms and expressions can be multiplied in the same way as numbers.

a \times a = a^2

b \times b = b^2 etc

Remember that 2a is not the same as a^2

2a = 2 \times a

a^2 = a \times a

In general, a^m \times a^n = a^{(m + n)}

Question

Simplify:

a) a^2 \times a^3

b) p^4 \times p^2

a) a^2 = a \times a and a^3 = a \times a \times a, so:

a^2 \times a^3 = a \times a \times a \times a \times a = a^5

Alternatively, using the general rule: {a}^{2}\times{a}^{3}={a}^{(2+3)}={a}^{5}.

b) p^4 \times p^2 = p^{(4 + 2)} = p^6

x is the same as x^1 when using this rule, eg n^3 \times n = n^{(3 + 1)} = n^4

Multiplying numbers and letters

Multiply letters and the numbers separately:

2 \times 3a means 2 \times 3 \times a which is 6a

4a \times 5a means 4 \times a \times 5 \times a which is 4 \times 5 \times a \times a = 20a^2

Question

Simplify 2p \times 3p^2

2p \times 3p^2

= 2 \times p \times 3 \times p \times p

= 2 \times 3 \times p \times p \times p

= 6p^3

Or, an alternative method would be:

2 \times p \times 3 \times p^2

2 \times 3 \times p \times p^2

= 6p^3