RULES FOR MULTIPLICATION OF ALGEBRAIC EXPRESSION
You know that, the product of a literal multiplied by itself is a power of the literal and that the index of the power is the number of times the literal is multiplied by itself.
Thus, a X a X a X a X a = a⁵ and a X a X a = aᶟ
Then, a⁵ X aᶟ = a⁸ = a X a X a X a X a X a X a X a = a⁸
We can generalize this as follows,
aᵐ X aⁿ = aᵐ⁺ⁿ, we can express this as, the product of two powers (xᵐ and xⁿ) of a variable x is another power (xᵐ⁺ⁿ) of the variable x whose index (m+n) is the sum of their indices (m & n).
Similarly, aᵐ X bⁿ X cᵖ = aᵐ bⁿ cᵖ
aᵐ X aⁿ X aᵖ = aᵐ⁺ⁿ X aᵖ = aᵐ⁺ⁿ⁺ᵖ
Multiplication of two or more Monomials-
To multiply two or more monomials, remember –
Product of two monomials = (product of numerical factors) X (product of variable factors)
The sign of the product is determined by the usual convention –
(+) X (+) = (+), (+) X (-) = (-), (-) X (-) = (+), (-) X (+) = (+)