Multiplying Algebraic Expressions

Multiplication

Multiplication does not concern itself with like terms, we can simply follow basic multiplication rules, multiply constants with constants, variables with variables etc.

When multiplying variables, we follow indices rules, when the base is the same but the power is different, add the powers together.

$$x^px^q=x^{p+q}$$

Let's have a look at some examples :

$$(3x)(5x)=15x^2$$ $$(-3ab)(ab)=-3a^2b^2$$

Multiplication has an interesting property when paired with addition of subtraction, the law of distribution.

$$a(b+c)=ab+ac \\ a(b-c)=ab-ac$$

This law is very powerful because it let's us expand brackets. That is, when we want to multiply two brackets, the first bracket distributes amongst each term in the second bracket. For example :

$$(2x+4)(x+2)$$ $$(\underbrace{2x+4}_{a})(\underbrace{x}_{b}+\underbrace{2}_{c})$$

Now distribute $a$ amongst $b$ and $c$.

$$x(2x+4)+2(2x+4 )\\ 2x^2+4x+4x+8 \\ 2x^2+8x+8$$