Looking at the diagram, we can write an expression that represents the total area of the rectangle.
18+6x+12Notice that we can simplify the expression that we got. Let's do it!
Next, we will write this expression in factored form using the greatest common factor (GCF). Recall that an algebraic expression is in factored form when it is expressed as the product of its factors. Let's start by writing the prime factorization of 6x and 30.
rcl
6x & = & 2* 3* x [0.2em]
30 & = & 2 * 3 * 5
The GCF of 6x and 30 is the product of the prime factors that are common to these monomials.
rcl
6x & = & 2* 3* x [0.2em]
30 & = & 2 * 3* 5 [0.5em]
GCF & = & 2 * 3 = 6
We got that the GCF of 6x and 30 is 6. Next, we will write each monomial as a product of the GCF and its remaining factors and use the Distributive Property to factor out the GCF.
6x+30 = 6 * x + 6 * 5 = 6(x+5)
The total area of the rectangle, written in factored form, is equal to 6(x+5) square units.
